Here we analyze three well-known conjectures: (i) the existence of infinitely-many twin primes, (ii) Goldbach’s strong conjecture, and (iii) Polignac’s conjecture. We show that the three conjectures are related to each other. In particular, we see that in analysing the validity of the Goldbach’s strong conjecture, one must consider also the existence of an infinite number of twin primes. As a consequence of how we approach this analysis, we also observe that if this conjecture is true, then so is Polignac’s conjecture. Our first step is an analysis of the existence of infinitely-many twin primes numbers. For this, using the formula 4((n−1)!+1) ≡ −n (mod n(n + 2)) – satisfied if and only if (n, n + 2) are twin primes –, together with Wilson’s theorem, we obtain conditions that must be met for two numbers to be twin primes. Our results, obtained from an analytic and functional study, lead us to conclude that there may exist infinitely-many twin primes. Next, we consider the validity of the Goldbach’s strong conjecture. After showing that the conjecture is true for the first even numbers, we notice a pattern that we analyze for any even number, reducing it to three cases: (i) when the even number 2n is two times a prime number n; (ii) when the even number 2n is such that n = 2m, with 2m − 1 and 2m + 1 twin primes; (iii) all other cases, i.e., for any 2n even number ∀n ∈ N with n > 1, n prime or not, with independence of n = 2m being 2m−1 and 2m+1 twin primes or not. In this last case we show that one can always find a certain r ∈ N such that 1 < r < n satisfying that n−r and n+r are primes, so that their sum is 2n. In this case we use the reduction to absurd method, and our results lead us to conclude that Goldbach’s strong conjecture is true to the best of our calculations, as well as the Polignac’s conjecture.

The question of what generates conscious experience has mesmerized thinkers since the dawn of humanity, yet its origins remain a mystery. The topic of consciousness has gained traction in recent years, thanks to the development of large language models that now arguably pass the Turing test, an operational test for intelligence. However, intelligence and consciousness are not related in obvious ways, as anyone who suffers from a bad toothache can attest - pain generates intense feelings and absorbs all our conscious awareness yet nothing particularly intelligent is going on. Still, in the hard sciences, this topic is frequently met with skepticism because to date no protocol to measure the content or intensity of conscious experiences in an observer-independent manner has been agreed upon. Here we present a novel proposal: Conscious experience arises whenever a quantum mechanical superposition forms. Our proposal has several implications: First, it suggests that the structure of the superposition determines the qualia of the experience. Second, quantum entanglement naturally solves the binding problem, ensuring the unity of phenomenal experience. Finally, a moment of agency may coincide with the formation of a superposition state. We outline a research program to experimentally test our conjecture via a sequence of quantum biology experiments. Applying these ideas opens up the possibility of expanding human experience through brain-quantum computer interfaces.

We use binary string to represent a natural number and show the composite procedure of odd-number and even-number functions, thus we propose full binary directed tree to represent the set of natural numbers and give another partition the natural number set to three sets: pure odd, pure even and mixed number. For the Collatz conjecture we make use of the parity of a natural number to analyse the sequence of iteration (or composite) of Collatz function and reduced Collatz function analog to the inverse function. We give tabular and binary strings to the algebra expression to state the sequence of Collatz, this is the key topic to proof the conjecture: the discrete powers of 2 can be changed to ultimately continuous powers of 2, finally get to pure even number and to the smallest number 1. The sequence created by the infinite iterations of the Collatz function becomes the ultimately periodic sequence if any natural number is the beginning value, proving the conjecture that has been held for 87 years.

We introduce a full binary directed tree structure to represent the set of natural numbers, further categorizing them into three distinct subsets: pure odd numbers, pure even numbers, and mixed numbers. We adopt a binary string representation for natural numbers and elaborate on the composite methodology encompassing odd- and even-number functions. Our analysis focuses on examining the iteration sequence (or composition) of the Collatz function and its reduced variant, which serves as an analog to the inverse function, to scrutinize the validity of the Collatz conjecture. To substantiate this conjecture, we incorporate binary strings into an algebraic formula that captures the essence of the Collatz sequence. By this means, we transform discrete powers of 2 into continuous counterparts, ultimately culminating in the smallest natural number, 1. Consequently, the sequence generated through infinite iterations of the Collatz function emerges as an eventually periodic sequence, thereby validating an enduring 87-year-old conjecture.

This paper presents an analysis of the number of zeros in the binary representation of natural numbers. The primary method of analysis involves the use of the concept of the fractional part of a number, which naturally emerges in the determination of binary representation. This idea is grounded in the fundamental property of the Riemann zeta function, constructed using the fractional part of a number. Understanding that the ratio between the fractional and integer parts of a number, analogous to the Riemann zeta function, reflects the profound laws of numbers becomes the key insight of this work. The findings suggest a new perspective on the interrelation between elementary properties of numbers and more complex mathematical concepts, potentially opening new directions in number theory and analysis.

Let a,b,c be positive integers such that a²+b²=c², 2|b,gcd(a,b)=1. In 1956, Jesmanowicz conjectured that for any positive integer w, the only solution of (aw)^x+(bw)^y=(cw)^z in positive integers is (x, y, z) = (2, 2, 2). In this paper, based on Gaussian integer ring, we show that Je$\acute{s}$manowicz' conjecture is true for any positive integer

A proof is given showing the Collatz Conjecture is true for all positive integers. The proof was possible once the perspective of the proof was changed from looking at the pattern of the positive integers to looking at the conjecture rules. The conjecture rule for even numbers organizes all positive integers into unique sets and the rule for odd numbers interconnects the unique sets into dendritic pathways to “1.” Infinite loops, other than the minor 4-2-1 loop after reaching “1,” and pathways to infinity are shown to be mathematically impossible. The proof predicted a general equation that shows all positive integers ultimately reach a final value of “1," and calculates the values and locations of the odd positive integers during the iterations for each tested positive integer.

It is proved that there exist two odd prime numbers, p_i and p_j , such that p_i + p_j = 2r + 2(r ⩾ 2), where p_n denote the n-th odd prime number, 1 ⩽ i, j ⩽ n. By the theory of generating functions, we prove that there exist two positive integers, h_i and h_j , such that h_i + h_j = r(r ⩾ 2), where h_n = (p_n − 1)/2，(p_n ⩾ 3).Then we complete the proof.

In this paper we present two ways to solve the Jacobian conjecture. The first way is an equivalent statement to the Jacobian conjecture using idempotent ideals. The second way is to use an equivalent thesis to the thesis of the Jacobian conjecture. In both cases we will show that the Jacobian conjecture is true.

This paper asserts that the falsity of Goldbach Conjecture results in the breakdown of Trichotomy Law. Assuming that Goldbach Conjecture breaks down at an even integer 2n, where n ≥ 3, we note that the differences of 2n with the odd primes in the interval (1, n) are composite integers. We form a product δ of the collection of the least prime factors of these composite integers. We show that for a base case this product breaks Trichotomy Law. With the inductive hypothesis that such is the case with 2n, we prove that for all even integers the breakdown of Goldbach Conjecture entails the breakdown of Trichotomy Law.

We develop a primality test for Mersenne numbers and investigate the primality of the sequence of Catalan-Mersenne numbers. We use induction as a proof to show that the 5th Catalan-Mersenne number is a prime number, thus demonstrating the infinitude of Mersenne primes.

Let $(\Omega, \mu)$, $(\Delta, \nu)$ be measure spaces and $\{\tau_\alpha\}_{\alpha\in \Omega}$, $\{\omega_\beta\}_{\beta \in \Delta}$ be 1-bounded continuous Parseval frames for a Hilbert space $\mathcal{H}$. Then we show that \begin{align}\label{UE} \log (\mu(\Omega)\nu(\Delta))\geq S_\tau(h)+S_\omega (h)\geq -2 \log \left(\frac{1+\displaystyle \sup_{\alpha \in \Omega, \beta \in \Delta}|\langle\tau_\alpha , \omega_\beta\rangle|}{2}\right) , \quad \forall h \in \mathcal{H}_\tau \cap \mathcal{H}_\omega, \end{align} where \begin{align*} &\mathcal{H}_\tau := \{h_1 \in \mathcal{H}: \langle h_1 , \tau_\alpha \rangle \neq 0, \alpha \in \Omega\}, \quad \mathcal{H}_\omega := \{h_2 \in \mathcal{H}: \langle h_2, \omega_\beta \rangle \neq 0, \beta \in \Delta\},\\ &S_\tau(h):= -\displaystyle\int\limits_{\Omega}\left|\left \langle \frac{h}{\|h\|}, \tau_\alpha\right\rangle \right|^2\log \left|\left \langle \frac{h}{\|h\|}, \tau_\alpha\right\rangle \right|^2\,d\mu(\alpha), \quad \forall h \in \mathcal{H}_\tau, \\ & S_\omega (h):= -\displaystyle\int\limits_{\Delta}\left|\left \langle \frac{h}{\|h\|}, \omega_\beta\right\rangle \right|^2\log \left|\left \langle \frac{h}{\|h\|}, \omega_\beta\right\rangle \right|^2\,d\nu(\beta), \quad \forall h \in \mathcal{H}_\omega. \end{align*} We call Inequality (\ref{UE}) as \textbf{Continuous Deutsch Uncertainty Principle}. Inequality (\ref{UE}) improves the uncertainty principle obtained by Deutsch \textit{[Phys. Rev. Lett., 1983]}. We formulate Kraus conjecture for 1-bounded continuous Parseval frames. We also derive continuous Deutsch uncertainty principles for Banach spaces.

The purpose of this paper is to study the sliding mode control as a Ricci flow process in the context of a three-story building structure subjected to seismic waves. The stability conditions result from two Lyapunov- functions, the first associated with slipping in a finite period of time, and the second with convergence of trajectories to the desired state. Simulation results show that the Ricci flow control leads to the minimization of the displacements of the floors. 3D Ricci solitons projection via a semi-conformal mapping to a surface is also studied.

A prime gap is the difference between consecutive prime numbers. The $n^{\text{th}}$ prime gap, denoted $g_{n}$, is calculated by subtracting the $n^{\text{th}}$ prime from the $(n+1)^{\text{th}}$ prime: $g_{n}=p_{n+1}-p_{n}$. Oppermann's conjecture is a prominent unsolved problem in pure mathematics concerning prime gaps. Despite verification for numerous primes, a general proof remains elusive. If true, the conjecture implies that prime gaps grow at a rate bounded by $g_{n}<{\sqrt {p_{n}}}$. This note presents a proof of Oppermann's conjecture using the Euler-Maclaurin formula on harmonic numbers. This proof simultaneously establishes Andrica's, Legendre's, and Brocard's conjectures.

We can analyze the properties of the Collatz Conjecture by using Terras’ Theorem, and computational graphical calculations. To do this, we introduce the concept of “tree" which shows the relationship between the input and output positive integers of the Collatz process. This approach offers a novel way for determining the non-existence of loops and diverge trees through computer simulations.

In 1937,German mathematician L.Collatz proposed the following conjeture:for any positive integer,if it is even,divide it by 2,if it is odd,multiply it by 3 and add 1 to get an even number.Continuing with the above rule, the final result will be 1.This paper gives a proof of this conjecture.

The Collatz conjecture (or 3n+1 problem) has been explored for about 86 years. In this article, we prove the Collatz conjecture. We will show that this conjecture holds for all positive integers by applying the Collatz inverse operation to the numbers that satisfy the rules of the Collatz conjecture. Finally, we will prove that there are no positive integers that do not satisfy this conjecture.

Collatz conjecture (3x+1 problem) is a natural phenomenon in set theory that may be reconstructed using known combinatorics and order theory. Construction begins by selecting a specific order isomorphism with a bijectional order-embedding. Mapping by 3x+1 induces a unique property to only members of the mapped embedding. Under selective congruence from recursive division by two, that complex controls sequence behavior. This demonstration uses an order isomorphism consisting of two linear orders: the (1) odd positive integers and the always odd (2) Rule 50 Jacobsthal numbers, as the embedding. The argument proceeds by cardinality. When the order isomorphism is mapped under 3x+1, all Rule 50 Jacobsthal numbers are mapped to all the powers of four. This one-to-one correspondence guarantees that every odd integer is assigned to a Rule 50 Jacobsthal number, and subsequently, to a power of four. To align this construction with the conjecture, expand the set to all positive integers by showing that: (1) the powers of four embed the powers of two, in a natural way, and (2) the unique factorization of any positive even integer, not congruent to a power of two, is simply an odd integer, once the factorized power of two is divided out. In other words, if the initial choice for a positive integer is not congruent to a power of two, then recursion continues until a Rule 50 Jacobsthal number (guaranteed by cardinality) is attained. Since this value mapped by 3x+1 is always a power of four, repeated division by two will always send the sequence to one. Because this same process occurs for any choice of positive integer, Collatz conjecture is true.

Since 1742, the year in which the Prussian Christian Goldbach wrote a letter to Leonhard Euler with his Conjecture in the weak version, mathematicians have been working on the problem. The tools in number theory become the most sophisticated thanks to the resolution solutions. Euler himself said he was unable to prove it. The weak guess in the modern version states the following: any odd number greater than 5 can be written as the sum of 3 primes. In response to Goldbach's letter, Euler reminded him of a conversation in which he proposed what is now known as Goldbach's strong conjecture: any even number greater than 2 can be written as a sum of 2 prime numbers. The most interesting result came in 2013, with proof of weak version by the Peruvian Mathematician Harald Helfgott, however the strong version remained without a definitive proof. The weak version can be demonstrated without major difficulties and will not be described in this article, as it becomes a corollary of the strong version. Despite the enormous intellectual baggage that great mathematicians have had over the centuries, the Conjecture in question has not been validated or refuted until today.

A twin prime numbers are two prime numbers which have the difference of 2 exactly. In other words, twin primes is a pair of prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Up to date there is no any valid proof/disproof for twin prime conjecture. Through this research paper, my attempt is to provide a valid disproof for twin prime conjecture.

Let $\mathbb{K}$ be a non-Archimedean (complete) valued field satisfying \begin{align*} \left|\sum_{j=1}^{n}\lambda_j^2\right|=\max_{1\leq j \leq n}|\lambda_j|^2, \quad \forall \lambda_j \in \mathbb{K}, 1\leq j \leq n, \forall n \in \mathbb{N}. \end{align*} For $d\in \mathbb{N}$, let $\mathbb{K}^d$ be the standard $d$-dimensional non-Archimedean Hilbert space. Let $m \in \mathbb{N}$ and $\text{Sym}^m(\mathbb{K}^d)$ be the non-Archimedean Hilbert space of symmetric m-tensors. We prove the following result. If $\{\tau_j\}_{j=1}^n$ is a collection in $\mathbb{K}^d$ satisfying $\langle \tau_j, \tau_j\rangle =1$ for all $1\leq j \leq n$ and the operator $\text{Sym}^m(\mathbb{K}^d)\ni x \mapsto \sum_{j=1}^n\langle x, \tau_j^{\otimes m}\rangle \tau_j^{\otimes m} \in \text{Sym}^m(\mathbb{K}^d)$ is diagonalizable, then \begin{align}\label{WELCHNONABSTRACT} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |\langle \tau_j, \tau_k\rangle|^{2m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{WELCHNONABSTRACT}) as the non-Archimedean version of Welch bounds obtained by Welch [\textit{IEEE Transactions on Information Theory, 1974}]. We formulate non-Archimedean Zauner conjecture.

Let $S=\left(s_1, \ldots, s_n\right)$ be a finite sequence of integers. Then $S$ is a Gilbreath sequence of length $n$, $S\in\mathbb{G}_n$, iff $s_1$ is even or odd and $s_2, \ldots, s_n$ are respectively odd or even and $\min\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\leq s_{m+1}\leq\max\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\forall m\in\left[\left.1, n\right)\right.$. This, applied to the order sequence of prime number $P$, defines Gilbreath polynomials and two integer sequences A347924 \cite{oeisA347924} and A347925 \cite{oeisA347925} which are used to prove that Gilbreath conjecture $GC$ is implied by $p_n-2^{n-1}\leqslant\mathcal{P}_{n-1}\left(1\right)$ where $\mathcal{P}_{n-1}\left(1\right)$ is the $n-1$-th Gilbreath polynomial at 1.

In this study, I examined the Beals conjecture on the basis of formulas that produce composite numbers, and I developed some other conjectures that, if answered, would be an answer to the Beals conjecture. Apart from this, I have examined the Beals conjecture from another perspective and posed The Germany Problem.

Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.

The Goldbach Conjecture, which is frequently termed as “1 + 1”, has been a fascinating goal for many mathematicians over centuries. A Chinese mathematician, Dr. Jingrun Chen, proved 1 + 2, which is a great success and the best result so far achieved. Although there were several attempts proving the conjecture, these attempts are either tediously long, complicated, or logically imperfect, thus not widely accepted. Taking advantage of the periodicity of primes, here the author provides a straight forward rigorous proof for the Conjecture.

A geometric Planck-scale model of quantum electrodynamics is tested against observations. Based on Dirac’s proposal to describe spin 1/2 particles as tethered objects, elementary fermions are conjectured to be fluctuating rational tangles with unobservable tethers. As Battey-Pratt and Racey showed, when such tangles propagate, they obey the free Dirac equation. Classifying rational tangles yields the observed spectrum of elementary fermions. Classifying deformations of tangle cores yields exactly three types of gauge interactions. They exchange three types of elementary gauge bosons and have the symmetry groups U(1), broken SU(2) and SU(3). The possible rational tangles for fermions, Higgs and gauge bosons allow only the observed Feynman diagrams. The complete Lagrangian of the standard model arises, including the Lagrangian of quantum electrodynamics. Over 50 tests of the tangle model are deduced. They include details on the perturbation expansion of the g-factor and the existence of limit values for electric and magnetic fields. Measurements agree with most tests, though this could change in the future. Some tests are genuine predictions that still need to be checked. In particular, the geometry of the process occurring at QED interaction vertices suggests an ab-initio estimate for the fine structure constant. In addition, the average geometric shapes of the elementary particle tangles suggest ab-initio lower and upper limits for the mass values of the electron and the other leptons.

Komlos conjecture is about the existing of a constant upper bound over the dimension n of the function $K(n)$ defined by $$K(n)=max_{ \{ \overrightarrow{V_1},...,\overrightarrow{V_n} \} \in \{ \overrightarrow{V_i} \in { R}^n \| \overrightarrow{V_i} \| \leq 1 \} ^n } min_{ \{\epsilon_1,...\epsilon_n\} \in \{-1,+1\}^n } \|\sum_{i=0}^{n} \epsilon_i \overrightarrow{V_i}\}\|_{\infty} $$ In this paper, the function $K(n)$ is evaluated first for lower dimensions, $n\leq 5$, where it found that $K(2)=\sqrt{2}$. For higher dimension, the function $f(n)=\sqrt{ n-\lceil\log_2(2^{n-1}/n) \rceil}$ is found to be a lower bound for the function $K(n)$, from where it is concluded that the Komlos conjecture is false i.e., the universal constant $k=max_{n \in N} K(n) $ does not exist because of $$\lim_{n \rightarrow \infty } K(n) \geq \lim_{n \rightarrow \infty } \sqrt{ \log_2(n)-1 }=+\infty$$

The Collatz conjecture, a longstanding mathematical puzzle, posits that, regardless of the starting integer, iteratively applying a specific formula will eventually lead to the value 1. This paper introduces a novel approach to validate the Collatz conjecture by leveraging the binary representation of generated numbers. Each transition in the sequence is predetermined using the Collatz conjecture formula, yet the path of transitions is revealed to be intricate, involving alternating increases and decreases for each initial value. The study delves into the global flow of the sequence, investigating the behavior of the generated numbers as they progress toward the termination value of 1. The analysis utilizes the concept of probability to shed light on the complex dynamics of the Collatz conjecture. By incorporating probabilistic methods, this research aims to unravel the underlying patterns and tendencies that govern the convergence of the sequence. The findings contribute to a deeper understanding of the Collatz conjecture, offering insights into the inherent complexities of its trajectories. This work not only validates the conjecture through binary representation but also provides a probabilistic framework to elucidate the global flow of the sequence, enriching our comprehension of this enduring mathematical mystery.

Reptilians or reptoids are staple characters of Hollywood cinema, science fiction literature, ufology and conspiracy theories. Despite its popularity, the reptoid has been dismissed by the scientific community as a figment of the imagination; born out of a speculation, paranoia and wanton anthropocentricism. In this paper, however, the Life Sequence Conjecture is advanced as a supportive framework for the notion of reptilian extraterrestrials. This paper is not an argument in support of the existence of extraterrestrials. Rather, it proposes that if extraterrestrials do exist, then a reptilian morphology is not untenable.

Build a special identical equation, use its calculation characters to prove and search for solution of any odd converging to 1 equation through (*3+1)/2^k operation, change the operation to (*3+2^m-1)/2^k, and get a solution for this equation, give a specific example to verify. Thus prove the Collatz Conjecture is true. Furthermore, analysis the sequences produced by iteration calculation during the procedure of searching for solution, build a weight function model, prove it decrease progressively to 0, build a complement weight function model, prove it increase to its convergence state. Build a (*3+2^m-1)/2^k odd tree, prove if odd in (*3+2^m-1)/2^k long huge odd sequence can not converge, the sequence must outstep the boundary of the tree after infinite steps of (*3+2^m-1)/2^k operation.

The Collatz conjecture is a well-known number theory puzzle that states that every positive integer would eventually converge to the trivial cycle of 1, 2, 1, 2,... when repeatedly exposed to a particular transformation. In this transformation, even numbers are divided in half, odd numbers are tripled, and one is added. In this study, we present a new method for creating a directed graph and using it to display and analyze Collatz sequences. Our technique creates what we call a Collatz directed graph by joining an endless number of simple directed graphs, each of which corresponds to a natural number. We show by careful mathematical analysis that all positive integers are included in this Collatz directed graph. Moreover, we give an evidence that verifies the Collatz conjecture by showing that the sole cycle in this graph is the trivial cycle of 1, 2, 1, 2,... We also prove that there is no sequence that diverges to infinity in this graph. Our results provide insights into the fundamental structure of Collatz sequences and further our knowledge of the Collatz conjecture .

In this paper, a short survey of the existed results concerning the Jacobian Conjecture is first given. Then the 3-fold linear type polynomial map will be analyzed in detail. The expansion of the Jacobian condition is deduced to obtain its equivalent algebraic equations, and the Jacobian condition will be analyzed to derive two coordinate transformations that can maintain the invariance of the Jacobian condition. Finally, it is proved by mathematical induction method that one general chain expression presented in this paper is just the inverse polynomial map of 3-fold linear type polynomial map, i.e. LJC(n,[3]) holds such that the Jacobian Conjecture holds.

The following is the Collatz Conjecture: Suppose we begin with a positive number, multiply it by 3 and add 1 if it is odd, and divide it by 2 if it is even. Then continue doing this as long as you can. Will it matter where you start, whether you end up at the number 1? The Collatz conjecture has been studied for around 85 years. We transform the Collatz function from decimal to binary, then use the binary string's character to prove the Collatz conjecture. In addition, we use mathematics to give another interpretation to chaos, which is the ultimately periodic positive integer sequence.

In this paper, we examine the weak abc conjecture and the strong abc conjecture using some functions. we attempt to discuss the possibilty that the negative consequence of the weak abc conjecture. Namely, we derive that the weak abc conjecture is not true. Additionally, we show that the strong abc conjecture is not true.

The Harmonic Graphs Conjecture states that there exists an asymptotic relation involving the Harmonic Index and the natural logarithm as the order of the graph increases. This conjecture, grounded in the novel context of Prime Graphs, draws upon the Prime Number Theorem and the sum of divisors function to unveil a compelling asymptotic connection. By carefully expanding the definitions of the harmonic index and the sum of divisors function, and leveraging the prime number theorem's approximations, we establish a formula that captures this intricate relationship. This work is an effort to contribute to the advancement of graph theory, introducing a fresh lens through which graph connectivity can be explored. The synthesis of prime numbers and graph properties not only deepens our understanding of structural complexity but also paves the way for innovative research directions.

In this paper, I introduce a new concept of representing numbers in base ; in other words, I have found new series for any number similar to series that could be written according to the collatz sequence which is called zi(n) in this article. These series need to end with 1. Then, we use two sets of rules to make a diagram which then proves the existence of such series for any number.In this diagram, by branching numbers into different branches in accordance to the modularity of 4 and continuing branching to the point that their numbers have enough common terms in their collatz series, we could reduce zi(n) to zi(k) so that k<n in any branch by Rule Number One. This diagram shows that zi(n) exists for every number, in other words, this proves the theorem (A) or zi-existence theorem. The proof of zi-existence theorem leads to a proof of the collatz conjecture because the collatz series could be written as a linear combination of such series that all of them end with 1, so the collatz series for any number ends with 1.

We investigate the value distribution of dierence polynomials of entire and meromorphic functions, which can be viewed as the Hayman's conjecture. And we also study the uniqueness of dierence polynomials sharing a common value.

In this article we have constructed a basic methodology from which important perspectives for both the Collatz conjecture and Beal's conjecture can be derived. We falsified the conjecture we previously developed on Beal's conjecture and made the falsified conjecture usable for Collatz conjecture. In this regard, we have clearly expressed the numbers that can reach 1 in the Collatz conjecture. Then, using this, we created a limit for the numbers that should be considered for the Collatz conjecture. Thanks to the analysis of this limit, we have clearly expressed the recursive Collatz function in an equation. Using this structure, we wrote a function that indicates how many times the Collatz function repeats certain numbers to reach 1.

Starting with a positive odd integer $n$, apply a function $f(n)$ repetitively such that $f(n) = 3n + 1$ if $n \not\equiv 0 (\text{mod}\:2)$ or $f(n) = n/2$ if $n \equiv 0 (\text{mod}\:2)$. Let the sequence of all the odd integers obtained form an orbit $n, f^1(n) , f^2(n), \ldots, f^k(n), f^{k + 1}(n)$. The $k^{th}$ odd integer is written as $f^k(n) = (3^k + \mathbf{B(k)})/2^{\mathbf{z(k)}}$ where $\mathbf{B(k)}$ is the collection of terms without the coefficient $n$. We show that when $1 - \mathbf{B(k)}/(2^{\mathbf{z(k)}} n) \approx 1$, the condition for unbounded orbit is given by OEIS A022921. Further, if there exists at least one orbit for which $f^{k + 1}(n) = n$ when $(k + 1) < 3$, we show that there exists no orbit with $k + 1 > 3$ for which $f^{k + 1}(n) = n$. The final result is that the odd integers that can violate the Collatz conjecture are smaller than 5.

In this paper, we demonstrate the Collatz conjecture using the mathematical complete induction method. We show that this conjecture is satisfied for the first values of natural numbers, and in analyzing the sequence generated by odd numbers, we can deduce a formula for the general term of the Collatz sequence for any odd natural number n after several iterations. This formula is used in one case that we analyze using the mathematical complete induction method in the process of demonstrating the conjecture.

This paper discusses a possible approach to validate the Goldbach conjucture which states that all even numbers can be expressed as a summation of two prime numbers. For this purpose the paper begins with the concept of successive-addition-of-digits-of-an-integer-number (SADN) and its properties in terms of basic algebraic functions like addition, multiplication and subtraction. This concept of SADN forms the basis for classifying all odd numbers into 3 series- the S1, S3 and S5 series- which comprise of odd numbers of SADN(7,4,1), SADN(3,9,6) and SADN(5,2,8) respectively and follow a cyclical order. The S1 and S5 series are of interest in the analysis since they include both prime and composite numbers while the S3 series exclusively consists of composite numbers. Furthermore, the multiplicative property of SADN shows why composites on the S1 series are derived as products of intra-series elements of the S1 and S5 series while composites on the S5 series are derived as products of inter-series elements of the S1 and S5 series. The role of SADN is also important in determining the relevant series for identifying the combination of primes for a given even number since it shows why such combinations for even numbers of SADN(1,4,7) will be found on the S5 series while those for even numbers of SADN(2,5,8) will lie on the S1 series and both the series have a role to play in identifying the prime number combinations for even numbers with SADN(3,6,9). Thereafter, the analysis moves to calculating the total number of acceptable combinations for a given even number that would include combinations in the nature of two composites (c1+c2), one prime and one composite (p+c) and two primes (p1+p2). A cyclical pattern followed by even numbers is also discussed in this context. Identifying the c1+c2 and p+c combinations and thereafter subtracting them from the total number of combinations will yield the number of p1+p2 combinations. For this purpose the paper discusses a general method to calculate the number of composites on the S1 and S5 series for a given number and provides a detailed method for deriving the number of c1+c2 combinations. The paper presents this analysis as a proof to validate the Goldbach conjecture. Since even numbers can be of SADN 1 to 9 and the relation between nTc (i.e. total number of acceptable combinations) and nc(i.e. number of composites) for all even numbers can either be of nTc > nc or nTc ≤ nc, the paper shows that the Goldbach conjecture is true for both these categories of even numbers. In this manner this analysis is totally inclusive of all even numbers in general terms and since the analysis of every even number is common in methodology but unique in compilation, apart from being totally inclusive, it is also mutually exclusive in nature. This proves that the Goldbach conjecture which states that all even numbers can be expressed as atleast one combination of two prime numbers holds true for all even numbers, across all categories possible. Additionally this approach proves that the identification of p1+p2 combinations which would validate the Goldbach conjecture lies in the identification of c1+c2 combinations.

For any positive integer n ≥ 2, the Erdős-Straus Conjecture claims that the Diophantine equation 4/n = 1/x + 1/y + 1/z has a solution where x, y, z are also positive integers. In this paper, a directed network based on this equation is generated, with properties such as its average clustering coefficient, average path length, degree distributions, and largest strongly connected component analysed to reveal some underlying trends about the nature of the conjecture. Potential connections between different numbers, that result from satisfying a source-solution relationship for this equation, are described using the appropriate number-theoretic interpretations wherever possible, while conjectures backed by these trends are made in other instances. Additionally, a directed configuration model is used to show that the origin of several results is the degree sequence of the network. Metrics relating to the prime number nodes, specifically their in and out degrees, are also explored to yield some intriguing observations. On the whole, the aim is to highlight the viability of complex networks as a computational tool to study this general class of problems pertaining to fixed-length unit fraction splits.

This paper addresses the Collatz Conjecture, an open question in mathematics that postulates all positive integers will eventually reach one when a pair of specific operations are repeatedly applied. Despite its apparent simplicity, the conjecture lacks a formal proof. To tackle this enigma, we introduce Algebraic Inverse Trees (AITs), data structures that trace inverse operations of the Collatz sequence. This new approach not only elaborates our unique methodology but also sheds light on the underlying complexities of the Collatz Conjecture.

In this article we propose the integral, series and product representations for the Ramanujan zeta-function. We suggest a variant for the Conrey-Ghosh product for the entire Ramanujan zeta-function. We present some variants for the product for the Ramanujan $\Xi$-function. We prove that all of its zeros are real. Along the way we obtain the truth of the Riemann-Hardy conjecture.

The two main strategies used in this study are the binary representation and the decomposition of a natural number into many compound functions of odd function and even function. The Collatz conjecture regarding odd even numbers in number theory can be examined and discussed using them in this way: The sequence created by the finite iterations of the Collatz function becomes the ultimately periodic sequence if any natural number is the beginning value, proving the conjecture that has been held for 85 years.

In this paper we study a conjecture proposed by P.Duxbury , C.laror , L.Leduino de Salles Neto in 2021\cite{conjecture} on the Golumb Ruler Problem which is a classical optimization model in discrete case . In \cite{conjecture} the authors constucted a continuous model for the Golumb Ruler Problem associated to the discrete case and conjectured that the optimal value of both cases are equal . We deal with this conjecture via algebraic geometrical methods .

For the solution existence condition of the Navier-Stokes equation, we propose a conjecture as follows: "\emph{The Navier-Stokes equation has a solution if and only if the determinant of flow velocity gradient is not zero, namely $\det (\bm \nabla \bm v)\neq 0$.}"

This article presents a rigorous approach to the Collatz Conjecture, focusing on fundamental properties of Collatz sequences. We establish key properties of the Collatz function and its inverse, including surjectivity and injectivity. The structure of Collatz sequences is analyzed in depth, proving important results such as the Bounded Subsequence Property and the uniqueness of cycles. Central theorems on the properties of Collatz sequences, including the boundedness of all sequences and the nature of the unique cycle, are presented and proved. These results culminate in a complete resolution of the Collatz Conjecture, demonstrating that all Collatz sequences eventually reach the cycle {1, 4, 2}. We provide a rigorous proof of the conjecture, while emphasizing the need for thorough peer review and verification by the mathematical community given the significance of this long-standing problem.

In experimental physics, we understand time as the duration of material changes that run into space. This fact is the standpoint for our model of time-invariant space in which causality is only a principle and not a physical actuality, and entropy runs only in space and not in time. Time is merely a duration of entropy that is increasing in time-invariant space. Time is entering existence when measured by the observer. In time-invariant space, motion happens only in space and not in time which means that also in open timelike curves motion happens only in space and not in time.

At the end of 2018, a high school student asked a question in Zhihu community, claiming that he had proved Goldbach's conjecture. The problem caused an explosive reaction and a large number of users participated in the discussion. And has caused the widespread influence. On January 1, 2019, the questioner issued his "proof". His proof was soon proved wrong. The heated discussion caused by the incident contains a lot of information of social science analysis value. Therefore, we follow up the event in the first time and build a time series dataset for the event. Taking the questioner's "proof" as the dividing line, all the answers, comments, sub comments and user information of writing these texts before and after two days were recorded. This series of temporal information can reflect the dynamic features of the interaction between user opinions, and the impact of exogenous shocks (proof release) on community opinions. The dataset can be used not only for the demonstration of various social network analysis algorithms, but also for a series of natural language processing tasks such as fine-grained sentiment analysis for long texts, as well as multimodal tasks combining natural language processing and social network analysis. This paper introduces the characteristics and structure of the dataset, shows the visualization effect of social network, and uses the dataset train the benchmark model of emotion analysis.

This article contains the theorems concerning the algebraic dependence of polynomial mappings with the constant Jacobian having two zeros at infinity. The work is related to the issues of the classical Jacobian Conjecture. This hypothesis affirm that the polynomial mapping of two complex variables with constant non-zero Jacobian is invertible. The Jacobian Conjecture is equivalent to the fact that polynomial mappings with constant non-zero Jacobian do not have two zeros at infinity, therefore it is equivalent to the two theorems given in the work. The proofs of these theorems proceeds by induction.

In this article, we present solutions for one of the oldest mathematical problems, the Collatz Conjecture, and provide a proof for the Riemann Hypothesis, utilizing a new number theory based on newly discovered number properties, which will also be presented in this paper. This is made possible through the Sophy-Peter mathematical framework, built upon this new number theory. The Collatz Conjecture will be disproven, but as an alternative, the Oscillating Theorem will be introduced, with its correctness proven within this article. Furthermore, we present the general version of the Riemann zeta function, developed based on the new number theory. The correctness of this function is verified by comparing it with existing results of the zeta function. Using this approach and the Sophy-Peter framework, we have successfully proven the Riemann Hypothesis, long considered a millennium problem. Moreover, since the general zeta function is proven, this implies the correctness of the new number theory and the Sophy-Peter framework.

The present study aims to show on the one hand how easily one can get confused when doing research on the internet. Different platforms, fora and homepages supply the visitor with different - and sometimes contradictory - information. On the other hand, we show how to overcome these contradictions and produce valuable research based on almost all sources. For our study, we use the example of the Feit-Thompson conjecture, which is - in opposite to the well-known Feit-Thompson theorem - not widely known. We try to clarify the scientific literature on this topic and we embed our own result into the present state of art. We prove that pq−1p−1 does not divide qp−1q−1 if p and q are twin primes, i.e. p=q+2. Thus we prove that the Feit-Thompson conjecture is true for twin prime numbers.

Lie algebra plays an important role in the study of singularity theory and other field of sciences. Finding numerous invariants linked with isolated singularities is always a main interest in the classification theory of isolated singularities. Any Lie algebra that characterizes simple singularity produces a natural question. The study of properties such as to find the dimensions of newly defined algebra is a remarkable work. Hussain, Yau and Zuo \cite{HYZ10} have been found a new class of Lie algebra \texorpdfstring{ $ \mathcal{L}_ k (V)$}{LG}, \texorpdfstring{$k\geq 1$}{LG} i.e., Der ($M_{k}(V), M_{k}(V)$) and purposed a conjecture over its dimension $\delta_{k}(V)$ for $k\geq0$. Later they proved it true for $k$ up to $k=1,2,3,4,5$. In this work, the main concern is whether it's true for a higher value of $k$. According to this, we calculate first, the dimension of Lie algebra \texorpdfstring{$\mathcal{L}_ k (V)$}{LG} for $k=6$ and then compute the upper estimate conjecture of fewnomial isolated singularities. Along with, we also justify the inequality conjecture: \texorpdfstring{$\delta_{k+1}(V) < \delta_{k}(V)$}{LG} for $k=6$. Our calculated results are innovative and a new addition to the study of singularity theory.

In solving the Collatz conjecture, it turns out that if we let all integers k be 6n, 6n+1, 6n+2, 6n+3, 6n+4, 6n+5, then we can solve the Collatz conjecture periodically. The Collatz conjecture states that for any positive integer P (initial value), if n is even, divide n by 2; if n is odd, repeat the rule of multiplying n by 3 and adding 1, which always converges to 1. One open problem has been proved by this paper. The authors hope to contribute to the mathematical community by presenting simple proofs of conjectures in the history of mathematics such as the Collatz conjecture.

Matiyasevich's theorem states that there is no algorithm to decide whether or not a given Diophantine equation has a solution in non-negative integers. Smorynski's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. We prove: (1) Smorynski's theorem easily follows from Matiyasevich's theorem, (2 ) Hilbert's Tenth Problem for Q has a negative solution if and only if the set of all Diophantine equations with a finite number of rational solutions is not recursively enumerable.

It is due to Littlewood that the truth of the Riemann theorem implies that of the Lindel\"{o}f conjecture. This paper aims to use the idea of Littlewood to prove the Lindel\"{o}f conjecture for the Riemann zeta function. The Lindel\"{o}f $\mu $ function at the critical line is zero, with use of the Riemann theorem for the entire Riemann zeta function, proved based on the work of Heath-Brown. Our result is given to show that the Lindel\"{o}f conjecture, connected with the proof of the moment conjecture, is true.

Twin prime numbers are two prime numbers which have the difference of 2 exactly. In other words, twin primes is a pair of prime that has a prime gap of two. Sometimes the part “twin prime” is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Up to date there is no any valid proof/disproof for twin prime conjecture. Through this research paper, my attempt is to provide a valid proof for twin prime conjecture.

We define the function $Col: \mathbb{N} \to \mathbb{N}$ as the Collatz function, given by $3n + 1$ if $n$ is odd and $\displaystyle\frac{n}{2}$ if $n$ is even \cite{Lagarias1990}. The conjecture postulates that for any positive integer, at some point, its iteration will reach 1, or equivalently, every orbit will fall into the periodic cycle $\{4, 2, 1\}$. Two conditions would invalidate the conjecture: the existence of a divergent orbit or the presence of another cycle. In 2019 Terence Tao \cite{tao} proved that almost all orbits converge to the trivial cycle of $\{1,4,2\}$, in this work we will prove the non-existence of divergent orbits. The central idea is to decompose the dynamic system $Col$ into a binary dynamic system, generated by different compositions of two functions. This differs from a typical dynamic system, which is generated by the iteration of a single function. We consider the system generated by the functions $\theta, \psi: \mathbb{R} \to \mathbb{R}$, defined as $\displaystyle\theta(x) = \frac{x}{2}$ and $\displaystyle\psi(x) = \frac{3x + 1}{2}$, denoted as $\langle \theta, \psi \rangle$. We examine sequences of functions in $\langle \theta, \psi \rangle$ of the form $S_k(x) = s_k \circ S_{k-1}(x)$ with $s_k \in \{\theta, \psi\}$. We define a function that assigns to each element of these sequences an integer, called the minimum value positive integer or simply the minimum value. This corresponds to the smallest positive integer $n$ such that $S_k(n)$ is an integer. As we will prove later, the minimum value is monotonically increasing, meaning that increasing the terms of the sequence will never result in a value lower than the previous one. Based on this behavior, we distinguish two types of sequences: stable ones, where the minimum value is constant from a certain point, and unstable ones, where the minimum value is divergent. The main result for unstable sequences is that when the slope of the sequence is divergent, the sequence is unstable. From this result, we can prove that there are no divergent orbits for the function $Col$.

In the bar of our Milky Way, there should be another supermassive black hole B which is with the mass almost 10−2~10−5 the Sgr A* and with a distance almost 10,000 lightyears from the Sgr A*. The bar is formed by the stars that are orbiting around the two black holes Sgr A* and B. And, in the bar, a lots of stars orbit around B while another lots of stars around Sgr A*. The two orbits form the peanut shape with “x-shaped structure” in the bar, while the boxy core is formed with all of the three orbits. And, the orbits of the stars out of the bar could be repulsed to a distant place by the black hole B to form the galactic spiral arms.

We consider mixture experiments in which the proportions of the components must be non-negative and their sum must equal one. Thus, the experimental region for a mixture of components is a simplex. Li and Zhang (2017) made the conjecture that the pseudo component transformation of the lattice points in the simplex has a special property. In this paper, we show that this conjecture is not true in general. Furthermore, we refine this conjecture and prove the refined conjecture.

In this research a neccessary and sufficient condition for the proof of the Binary Goldbach conjecture is established. It is established that the square of all natural numbers greater or equal to 2 have an additive partition equal to the sum of the square of a natural number greater or equal to zero and a Goldbach partition semiprime. All Goldbach partition semiprimes are odd except 4. This finding is in itself proof all composite even numbers have at least Goldbach partition. The result of the proof of the Binary Goldbach conjecture is used to prove the Andrica and Legendre conjectures. The Riemann hypothesis is examined and sources of non trivial zeroes outside the critical strip are discussed. An example example of a non-trivial zero outside the critical strip is given

The Yang-Mills conjecture addresses the fundamental nature of the strong force, one of the four fundamental forces in nature, responsible for binding quarks together to form protons, neutrons, and other hadrons. It was proposed in the early 1950s, the Yang-Mills suggests a mathematical framework for describing the behaviours of gauge fields, which are the carriers of fundamental forces. In particular, it focuses on non-abelian gauge theories, where the gauge fields themselves interact with each other. The non-abelian aspect refers to the fact that the order of operations matters when combining these gauge transformations, leading to a more intricate structure compared to abelian theories. This conjecture posits the existence and significance of certain mathematical structures, known as Yang-Mills fields, which play a crucial role in the formulation of the Standard Model of particle physics. The Standard Model describes the electromagnetic, weak, and strong nuclear forces, as well as the elementary particles that constitute matter. Despite its foundational importance, proving the Yang-Mills conjecture has proven to be a formidable challenge. The conjecture is intimately connected to the concept of mass gap, which refers to the idea that the particles involved in the strong force interactions exhibit mass, in contrast to the photon in electromagnetism, which is massless. The successful resolution of the Yang-Mills conjecture is expected to deepen our understanding of the nature of particle physics and may provide insights into the unification of fundamental forces. In this regard we hereby provide solutions to solve Yang-Mills conjecture using the method of Self Information Entanglement and Quantum Information Transport Equations to elucidate the origin of Universe from Unperceivable Information called “Avyaktham” through the emergence of perceivable information “Vyaktham”. For the first time in the world we provided an empirically verifiable solution to the origin of emergence and existence of Universe based on the methods to predict the emergence using working model of clinical Ayurveda. It is computed that the value of mass gap mentioned in Yang-Mills conjecture is around mYM = mbit ≈ 1.06×10⁻⁴¹kg.

Background: Early diagnosis of postoperative complications is an urgent task, allowing timely prescribing of appropriate therapy and reducing the cost of patient treatment. Prognostic models based on various data could help in the early diagnosis of postoperative complications after cardiac surgery. Objectives: The purpose of the study was to determine whether an integrated approach based on clinical data along with metabolites and biomarkers had greater predictive value than the models built on less data. Methods: The study included patients (n=62) admitted for planned cardiac surgery (coronary artery bypass grafting with cardiopulmonary bypass), who were retrospectively divided into two groups depending on the presence (n=26) or absence (n=36) of postoperative complications of all types. Clinical and laboratory data on the first day after surgery were analyzed. Additionally, patients' blood samples were collected before and on the first day after surgery to determine biomarkers (interleukin-6, procalcitonin, NT-proBNP, high-sensitivity troponin T) and metabolites (8 aromatic and 2 dicarboxylic acids were detected using gas chromatography-mass spectrometry). Results: Patients before surgery, compared with healthy donors, differed in the concentration of metabolites (p &lt; 0.05), and had concentrations of a number of biomarkers exceeding the corresponding reference values. Multivariate PLS-DA models, predicting the presence or absence of postoperative complications, were built using clinical data (ROC-AUC=0.71), concentrations of metabolites and biomarkers (ROC-AUC=0.60), and the entire data set (ROC-AUC=0.75). For comparison we built univariate models using the EuroScore2 (ROC-AUC=0.59) and SOFA (ROC-AUC=0.76) scales; concentrations of lactate (ROC-AUC=0.71), the dynamic changes of 4-hydroxyphenyllactic acid (ROC-AUC=0.69), and the sum of three sepsis-associated metabolites (ROC-AUC=0.70). The proposed complex model using entire data set was comparable to the SOFA scale, which confirms the expediency of searching for new predictive models based on a variety of factors.

Milk serves as a crucial source of natural bioactive compounds essential for human nutrition and health. The gastrointestinal digestion of milk proteins releases various biologically active peptides that positively impact human health and enhance physiological performance. With the growing production of cheese, Greek yogurt, and other dairy products, the volume of unutilized acid whey is significantly increasing. Acid whey, containing almost all whey proteins and approximately one-quarter of casein, presents a valuable raw material for generating peptides with potential health benefits. These peptides exhibit properties such as antioxidant, antimicrobial, anti-inflammatory, anticarcinogenic, antihypertensive, antithrombotic, opioid, mineral-binding, and growth-stimulating activities, contributing to improved human immunity and the treatment of chronic diseases. Enzymatic hydrolysis of milk proteins has been developed as a method to produce these peptides, facilitating their use in food fortification. To incorporate whey into functional beverages, it undergoes fermentation by lactic acid bacteria with proteolytic activity. To specifically enrich these beverages with peptides exhibiting targeted bioactivities, it is essential to select lactic acid bacteria strains possessing the requisite protease profiles. Additionally, the sensory properties of the final product can be enhanced using starter cultures with diverse metabolic capabilities, even in the absence of added flavoring agents. Given the imperative to develop waste-free technologies and enhance the profitability of the dairy industry, there is a growing need to efficiently utilize and transform acid whey into a broad spectrum of valuable products and food additives. This approach is justified not only by the nutritional benefits of the bioactive components in whey but also by the commercial potential of safe and health-enhancing products.

The paper focuses on the application of a multilevel, integrative and territorial approach to the protection of cultural heritage through planning instruments in Serbia. It points out the problems of the sectoral approach and discusses international recommendations that can be integrated into the planning methodology. The case study is the area of Djerdap National Park, which has an already established international and national importance. The research suggests that the cultural heritage in the area, with the exception of the Roman limes, is still recognized at the level of individual localities. The study emphasizes the importance of aligning all levels of governance to safeguard the whole spatial entity rather than focusing solely on its particular areas. The interna-tional and national importance of the planning area contributes to the strengthening of awareness of heritage and its institutional protection. However, the vitality of the area, which is key to its sustainable development, comes from the local level. Planning documents contribute to the inte-gration of local values and local communities into development programs and projects.

In order to shorten the detection time and improve the average precision on embedded devices, A lightweight and high accuracy model is proposed for passion fruit in complex environments (backlight, occlusion, overlap, sunny, cloudy, rainy). Firstly, replacing the backbone network of YOLOv5 with a lightweight GhostNet model reduces the number of parameters and computation while improving detection speed. Secondly, a new feature branch is added to the GhostNet network, and the feature fusion layer in the neck network is reconstructed to effectively combine the lower-level and higher-level features, which not only improves the accuracy of the model but also maintains its lightweight. Finally, the knowledge distillation methods are used to transfer the knowledge from the more capable teacher model to the less capable student model, which significantly improving the detection accuracy. The improved model is denoted as G-YOLO-NK. The average accuracy of the G-YOLO-NK network is 96.00%, which is 1.00% higher than the original YOLOv5s model. Furthermore, the improved model size is 7.14MB, reduced to half of the original model, and the real-time detection frame rate is 11.25 FPS on the Jetson Nano. Compared to the state-of-the-art model, the proposed model outperforms them in terms of average precision and detection performance. The present work provides an effective model for real-time detection of passion fruits in complex orchard scenes, which can provide valuable technical support for the development of orchard picking robots and greatly improve the intelligence level of orchards.

The impact of interaction SS with MJO on rainfall along Java Island to East Nusa Tenggara has been studied using daily rainfall observation data from 2140 weather observation stations, which are also equipped with GSMaP, OLR, and ERA5 data. There were 61 SS events found, 17 during active MJO and 44 in inactive MJO. Rainfall increases more in the western study area when the active MJO and more in the eastern study area when the inactive MJO is due to SS. SS reduces rainfall in the Jakarta region, regardless of the activity or inactivity of the MJO. SS causes extreme rainfall to only occur in a small part of certain areas, so it tends to significantly reduce the possibility of extreme rainfall. In the southern part of the IMC, SS predominates over MJO in supporting increased water vapor transport. Large-scale synoptic circulations like the monsoon, SS, and MJO can interact with local land-sea wind circulation to produce spatiotemporal variability in rainfall on Java Island. Rainfall mostly increases in the afternoon and decreases in the morning when SS occurs, whether there is MJO or not. Convective instability analysis indicates that SS increases precipitation, most likely by lowering CIN and raising VIMFC.

The Simultaneous Localization And Mapping (SLAM) scanner is an easy and portable Light Detection And Ranging (LiDAR) data acquisition device. Its main output is a 3D point cloud covering the scanned scene. Regarding the importance of accuracy in the survey domain, this paper aims to assess the accuracy of two SLAM scanners: the NavVis VLX and the BLK2GO Scanner. This assessment is conducted for both outdoor and indoor environments. In this context, two types of reference data are used: the Total Station (TS) and the static scanner Z+F Imager 5016. To carry out the assessment, four comparisons are tested: cloud to cloud, cloud to mesh, mesh to mesh, and edge detection board assessment. However, the results of the assessments confirm that the accuracy of indoor SLAM scanner measurements (5 mm) is greater than that of outdoor ones (between 10 mm and 60 mm). Moreover, the comparison of cloud to cloud provides the best accuracy regarding direct accuracy measurement without manipulations. Finally, based on the high accuracy, scanning speed, flexibility, and the accuracy differences between tested cases, it is confirmed that SLAM scanners are effective tools for data acquisition.

In recent years, electroencephalogram (EEG) emotion recognition has emerged as a research hotspot in the field of artificial intelligence (AI). Despite advancements in EEG-based emotion recognition, room for enhancing performance persists due to EEG signal redundancy and limitations in feature extraction, leading to inefficient models and emotional information loss. To fully utilize EEG's emotional information and improve recognition accuracy while reducing computational costs, this paper proposes a Convolutional-Recurrent Hybrid Network with a dual-stream adaptive approach and an attention mechanism (CSA-SA-CRTNN). Firstly, the model utilizes a CSAM module to assign corresponding weights to EEG channels. Then, an adaptive dual-stream convolutional-recurrent network (SA-CRNN and MHSA-CRNN) is applied to extract local spatial-temporal features. After that, the extracted local features are concatenated and fed into a temporal convolutional network with a multi-head self-attention mechanism (MHSA-TCN) to capture global information. Finally, the extracted EEG information is used for emotion classification. We conducted binary and ternary classification experiments on the DEAP dataset, achieving 99.26% and 99.15% accuracy for arousal and valence in binary classification, and 97.69% and 98.05% in ternary classification, surpassing relevant algorithms. Additionally, the model's efficiency is significantly higher than other models, achieving better accuracy with lower resource consumption.

Glycosidic linkage analysis was conducted on the unfractionated polysaccharides in the alcohol-insoluble residues (AIRs) prepared from six red seaweeds (Gracilariopsis sp., Prionitis sp., Mastocarpus papillatus, Callophyllis sp., Mazzaella splendens, and Palmaria palmata) using GC-MS/FID analysis of partially methylated alditol acetates (PMAAs). The cell walls of P. palmata primarily contained mixed-linkage xylans and small amounts of sulfated galactans and cellulose. In contrast, the unfractionated polysaccharides of the other five species were rich in galactans displaying diverse 3,6-anhydro-galactose and galactose linkages with varied sulfation patterns. Different levels of cellulose were also observed. This glycosidic linkage method offers advantages for cellulose analysis over traditional monosaccharide analysis that is known for underrepresenting glucose in crystalline cellulose. Relative linkage compositions calculated from GC-MS and GC-FID measurements showed that anhydro sugar linkages generated more response in the latter detection method. This improved linkage workflow presents a useful tool for studying polysaccharide structural variations across red seaweed species. Furthermore, for the first time, relative linkage compositions from GC-MS and GC-FID measurements, along with normalized FID and total ion current (TIC) chromatograms without peak assignments, were analyzed using principal component analysis (PCA) as a proof-of-concept demonstration of the technique's potential to differentiate various red seaweed species.

Background: Educating college students about the importance of good sleep habits could lead to the adoption of healthier sleep routines, including sufficient sleep duration and sleep quality. The current pre-post study examines the impact of completing a sleep education program called “Sleep 101” on (1) sleep hygiene practices, (2) sleep quality, and (3) weekday and weekend sleep behaviors among college students. “Sleep 101” is an interactive online course developed to educate college students about the importance of sleep by addressing basic sleep physiology, the impact of sleep on mood, academic and physical performance, the interactions between sleep and various substances, and common sleep disorders. Methods: 338 college students were recruited from a midsized public university in the US and invited to participate in “Sleep 101”, of which 25 participants completed the baseline and post-intervention questionnaire. The Sleep Hygiene Index (SHI) was utilized to evaluate sleep hygiene practices, while standard questions were employed to assess weekday and weekend sleep behaviors and overall sleep quality. Results: Those who completed the study demonstrated a significant increase in weekday sleep duration and were less likely to engage in negative prior bedtime activities. In addition, 40% of those who completed baseline and post-intervention assessments noticed improvements in their sleep quality. Conclusion: These findings suggest that a brief online program is beneficial in improving sleep behaviors among college and could be a scalable approach to addressing current sleep issues and preventing future sleep problems in college students.

The profile of secondary metabolites occurring in apple cuticular layer is not only characteristic for particular apple cultivar, but also dynamically reflects various external factors in growing environment. In this study, the possibility to authenticate apple samples based on analysis of their cuticular layer extracts was investigated. Ultra-high-performance liquid chromatography coupled to high resolution tandem mass spectrometry (UHPLC-HRMS/MS) was employed for obtaining metabolomic fingerprints. In total, 274 authentic apple samples, four cultivars harvested within the seasons 2020 to 2022 in the Czech Republic and Poland were analysed. The generated complex data processed by univariate and multivariate statistical methods enabled to build classification models for discrimination of apple cultivars as well as their geographical origin. The models showed very good performance in differentiation of Czech and Polish samples for three of four cultivars: ‘Gala’, ‘Golden Delicious’ and ‘Idared’, moreover, the validity of the models was verified over harvest seasons. The diagnostic markers, besides metabolites of triterpene biosynthetic pathway, mainly represented wax esters. ‘Jonagold’, which is known to be susceptible to mutations, was the only cultivar for which the unambiguous classification of geographical origin was not possible.

Superior fiber quality is one of the most important objectives in cotton breeding. To detect the genetic basis underlying fiber quality, an F2 population containing 413 plants was constructed by crossing Jifeng 914 and Jifeng 173, both of which have superior fiber quality, with Jifeng 173 being better. Five fiber quality traits were investigated in the F2, F2:3, F2:4, and F2:5 populations. Quantitative trait loci (QTL) mapping was conducted based on a high-density genetic map containing 11,488 single nucleotide polymorphisms (SNPs) and spanning 4,202.12 cM in length. Transgressive segregation patterns and complex correlations in the five tested traits were observed. A total of 108 QTLs were found, including 27 for fiber length (FL), 16 for fiber strength (FS), 24 for micronaire (MC), 17 for fiber uniformity (FU), and 24 for fiber elongation rate (FE). Chromosome A7 contained 12 QTL, ranking the first. No QTL was found on chromosome D1 and D11. Each QTL contributed 1.98%–21.45% to the phenotypic variation (PV), including 13 major effect QTLs that contributed more than 10% toward PV. Two QTLs could be repeatedly detected in three populations, including qFL-D3-2 in F2, F2:4, and F2:5 with 9.18%–21.45% of PV, qFS-A11-1 in F2:3, F2:4 and F2:5 with 6.05%–10.41% of PV. Another seven stable QTLs could be detected in two populations, including four major effect QTLs: qFL-A12-3, qFS-D10-2, qMC-D6-2, and qMC-D8-1. Fourteen QTL-overlapping regions were found, which might explain the complex correlations among the five phenotypic traits. Four regions on chromosome A11, D3, D6, and D10 covered by both stable and major effect QTLs are promising for further fine mapping. The genomic regions of the two QTLs detected in three populations and the four major effect QTLs contain 810 genes. Gene functional analysis revealed that the annotated genes are mainly involved in protein binding and metabolic pathways. Fifteen candidate genes in the qFL-D3-2 region are highly expressed in fiber or ovules during fiber initiation, elongation, secondary cell wall thickening, or maturation stages. qRT-PCR revealed that Ghir_D03G005440.1 and Ghir_D03G011310.1 may play a role in promoting fiber initiation, Ghir_D03G006470.1 may be beneficial for promoting fiber elongation. This study provides more information for revealing the molecular genetic basis underlying cotton fiber quality.

Currently there are fewer depth models applied to pepper picking detection, while the existing generalized neural networks have problems such as large model parameters, long training time, and low model accuracy.In order to solve the above problems, this paper proposes a Yolo-chili target detection algorithm for chili pepper detection. First, the classical target detection algorithm yolov5 is used as a benchmark model, and an adaptive spatial feature pyramid structure combining the attention mechanism and the idea of multi-scale prediction is introduced to improve the model's detection effect on occluded peppers and small target peppers. Secondly, a three-channel attention mechanism module is introduced to improve the algorithm's long-distance recognition ability and reduce the interference of redundant testers. Finally, the quantized pruning method is used to reduce the model parameters and realize the lightweight processing of the model. Applying the method to the homemade chili pepper dataset, the AP value of chili pepper reaches 93.11%; the accuracy rate is 93.51% and the recall rate is 92.55%.The experimental results show that yolo-chili is able to achieve accurate and real-time pepper detection under complex orchards.

The temporary immersion system bioreactor named GreenTray®[2], [3]presents advantages over the existing ones. Firstly, there is no need to use forceps to move the shoots or plantlets in or out of the recipient, neither the use of scalpel to divide them. Secondly, the basis of the shoot can remain in the GreenTray® and can sprout again in several cycles of growth. These two characteristics reduce the costs in the process of micropropagation. Besides, shoots or plantlets development is enhanced by the aeration of the recipient, thus enriching with CO2 the recipient atmosphere. The chapter describes and provides images and values of interest in (1) the micropropagation process of some commercial Prunus or Pyrus rootstocks; (2) the plantlet growth under autotrophic conditions; and (2) the inoculation of plants with pathogens that reproduce in vitro the symptoms observed in vivo, using the GreenTray® bioreactor.

Aiming at the problems of inaccurate segmentation of long object and information loss of small object in real-time semantic segmentation algorithm, this paper proposes a lightweight multi-branch real-time semantic segmentation network based on BiseNetV2. The new auxiliary branch makes full use of spatial details and context information to cover the long object in the field of view. Meanwhile, in order to ensure the inference speed of the model, the asymmetric convolution is used in each stage of the auxiliary branch to design a structure with low computational complexity. In the multi-branch fusion stage, the alignment and fusion module is designed to provide guidance information for deep and shallow feature mapping, so as to make up for the problem of feature misalignment in the fusion of information at different scales, and thus reduce the loss of small target information. In order to further improve the model’s awareness of key information, a global context module is designed to capture the most important features in the input data. The proposed network uses NVIDIA GeForce RTX 3080 Laptop GPU experiment, on the road street view data set Cityscapes and CamVid average occurring simultaneously ratio reached 77.1% and 78.4% respectively, with running speed of 127 frames/s respectively and 112 frames/s. The experimental results show that the proposed algorithm can achieve real-time segmentation and improve the accuracy significantly, showing good semantic segmentation performance

Excess nitrogen in agricultural drainage poses a serious threat to the water quality safety of the Yellow River basin. Utilizing aquatic plants to modify the rhizosphere microbial community structure and facilitate nitrogen transformation is a crucial strategy for mitigating regional water eutrophication. Our results revealed that the denitrification rate (DR), dissimilatory nitrate reduction to ammonium rate (DNRAR) and nitrogen fixation rate (NFR) of rhizosphere sediments exhibited a significant increase in artificially cultivated ditch. Compared with those in natural ditches, the richness of the bacterial community and the relative abundances of Bacteroidota, Verrucomicrobiota, Firmicutes, Anaeromyxobacter and Geobacter, which are involved mainly in the nitrogen cycle, in the rhizosphere sediments of artificially cultivated ditch were significantly greater due to improvements in environmental conditions. In artificially cultivated ditch, the dominant functional genes affecting DRNARs in the rhizosphere sediments of P. australis were nrfC and nrfA, while DRs were driven mainly by norB and napA, which were influenced by the nitrogen and carbon levels; and the dominant functional genes affecting NFRs in the rhizosphere sediments of T. orientalis were nifD, nifK and nifH. Our results provide a scientific basis for the use of aquatic plants for mitigating excess nitrogen levels in agricultural drainage.

Strawberry root rot caused by Neopestalotiopsis clavispora is one of the main diseases of strawberry and significantly impacts the yield and quality of strawberry fruit. There are now no effective control techniques available except for fungicide sprays, which may directly impact consumers. Biological control is becoming an alternative method for the control of plant diseases to replace or decrease the application of traditional synthetic chemical fungicides. Trichoderma is widely used as a biological agent for controlling strawberry root rot. In order to provide resources for screening the highly effective biocontrol fungus for controlling strawberry root rot caused by Neopestalotiopsis clavispora, the biocontrol mechanism,the control effects of Trichoderma asperellum CMT10 against strawberry root rot and growth-promoting effects on strawberry seedlings were investigated by plate culture, microscopy observation and root drenching methods.The results showed that CMT10 had obvious competitive, antibiotic and hyperparasitism effects on Neopestalotiopsis clavispora CMGF3. The CMT10 could quickly occupy nutritional space, and the inhibition rates of CMT10 against CMGF3 in confrontation culture on 7 d was 65.49%. The inhibition rates of volatile metabolite and fermentation metabolite produced by CMT10 against CMGF3 were 79.67% and 69.84%, respectively. The mycelium of strain CMT10 can act as hyperparasites by making contacting, winding and penetrating hyphae of CMGF3. Pot experiment showed that the biocontrol efficacy of CMT10 on strawberry root rot caused by Neopestalotiopsis clavispora was 63.00%. CMT10 had obvious promotion effect on strawberry growth, the plant height, root length, total fresh weight, root fresh weight, stem fresh weight and root dry weight, with the promotion rates were 20.09%, 22.39%, 87.11%, 101.58%, 79.82% and 72.33%, respectively. Overall, this study showed the ability of Trichoderma asperellum CMT10 to control strawberry root rot and their potential to develop as novel biocontrol agents to replace chemical fungicides for eco-friendly, sustainable agriculture.

In this paper we study a class of impulsive delayed neural networks with parameter uncertainties and reaction-diffusion terms. Using the properties of M-matrices and some inequality techniques, some sufficient conditions are derived to guarantee the global exponential stability of the given system. The results obtained are presented by simple algebraic inequalities, which are certainly more concise than previous methods. Finally, the validity and usefulness of our results are illustrated by arithmetic examples.

Pyrops candelaria is one of the common pests of fruit trees, but the research on the pathogenic microorganisms it may carry is very limited. Therefore, it is essential to reveal the pathogenic microbes it carries and their potential hazards. This study found a new virus from the transcriptome of P. candelaria, which was first reported in P. candelaria and named as PyCaV (Pyrops candelaria associated virus). RACE and bioinformatics assay revealed that the full-length of PyCaV is 10855 bp with the polyA tail, containing a single open reading frame (ORF) encoding a polyprotein consisting of 3171 amino acid (aa). The virus has a typical Iflavirus structure, including two rhv domains, a RNA helicase domain (HEL), a 3C cysteine protease domain (Pro), and a RNA-dependent RNA polymerase domain (RdRp). Further phylogenetic analysis revealed that this virus belongs to family Iflaviridae and sequence alignements analysis suggedted PyCaV is new member in unassigned genus of family Iflaviridae. Further in-depth analysis of virus-infection-part showed that PyCaV is distributing in the whole longan lanternfly, including its head, chest, and abdomen, but more PyCaV was identified in the chest. The distribution of PyCaV in different parts of P. candelaria was further explored, which showed that more PyCaV were detected in its piercing-sucking mouthparts and chest viscera. Statistical analysis showed that the PyCaV infection was affected by time and locations.

Apis mellifera, especially weak ones, are highly vulnerable to Carpoglyphus lactis mites, which can rapidly infest and consume stored pollen, leading to weakened colonies and potentially colony collapse. This study aimed to ascertain and investigate the prevalence of this mite in honeybee colonies across 9 provinces in the Republic of Korea (ROK). A total of 615 honeybee colonies were collected, from 66 apiaries during the spring and 58 apiaries during the summer of 2023. A 1,242 bp segment of the the Cytochrome c oxidase subunit 1 (COI) gene was amplified using the polymerase chain reaction method. The detection levels of C. lactis in the honeybees were compared between winter and summer. Based on the COI sequence analysis, the nucleotide sequence similarity of C. lactis mites isolated in the ROK with those from China (NC048990.1) was found to be 99.5%, and with those from the United Kingdom (KY922482.1) was 99.3%. This study is the first report of C. lactis in Korean apiaries. The findings in this study demonstrate a significantly higher detection rate in winter, which is 4.1 times greater than that in summer (p &lt; 0.001). Furthermore, the results underscore the usefulness of molecular diagnostic techniques for detecting C. lactis mites.

With the burgeoning growth of online retail, the issue of counterfeit products has become a significant threat to both consumer trust and brand integrity, posing challenges to sustainable market practices. Online retail platforms are promoted to redesign their channel structures and enhance brand traceability to tackle counterfeits using blockchain technology. To investigate the interactions between blockchain technology and the channel structures of online retail platforms, we design a game theory model incorporating a manufacturer with(out) blockchain participation selling products via an online retail platform that operates an agency channel and/or a reselling channel. We show that the critical trade-off of blockchain participation comprises the brand assurance effect of the blockchain, the channel competition intensification effect, and the blockchain adoption cost. The platform is capable of strategically designing the channel structure to encourage (while discouraging) blockchain participation by the manufacturer. Our analysis highlights the complementarity between blockchain participation and the channel structure. Furthermore, the effect of the consumer’s belief in the reselling channel, the commission fee in the agency channel, and the substitutability between channels are investigated in depth. The research provides valuable insights for online retail platforms and policymakers seeking to foster a sustainable and trustworthy e-commerce ecosystem.

In this paper, we extend the KdVSKR equations in (1+1)-dimension and (2+1)-dimension to fractional KdVSKR equations with modified Riemann-Liouville derivative. The (2+1)-dimensional KdVSKR equation, which is a recent extension of (1+1)-dimensional KdVSKR equation, can model the resonances of solitons in shallow water. By means of the Hirota bilinear method, finite symmetry group method and consistent Riccati expansion method, many new interaction solutions have been derived. Soliton-cnoidal interaction solution of the (1+1)-dimensional fractional KdVSKR equation has been derived for the first time. For the (2+1)-dimensional frac-tional KdVSKR equation, two-wave interaction solutions and three-wave interaction solutions, including dark-soliton-sine interaction solution, bright-soliton-elliptic interaction solution, and lump-hyperbolic-sine interaction solution, have been derived. Impact of the fractional order on the shapes of these solutions has been illustrated by figures. Three-wave interaction solutions of fractional systems have not been reported in the existing references. The research idea in this paper can be applied to other fractional differential equations.

COX II containing a dual core CuA active site is one of the three core subunits of mitochondrial Cco, which plays a significant role in the physiological process. In this report, the full-length cDNA of COXⅡ gene was cloned from Sitophilus zeamais, which had an ORF of 684 bp encoding 227 amino acids residues. The predicted COXⅡ protein had a molecular mass of 26.2 kDa with pI value of 6.37, and multiple sequence alignment and phylogenetic analysis indicated that Sitophilus zeamais COXⅡ had high sequence identity 78.51% with the COXⅡ of other insect species, especially similarity to sitophilus oryzae. This gene was subcloned into the prokaryotic expression vector pET-32a, and induced by IPTG in E.coli Transetta (DE3) expression system. Finally the COXⅡ with 6-His tag was purified using affinity chromatography with Ni²⁺-NTA agarose. WB showed the recombinant COXⅡ was about 44 kD, and the concentration of fusion protein was 50μg/mL. UV-spectrophotometer and infrared spectrometer analysis showed that recombinant COXⅡ could catalyze the oxidation of substrate Cytc, and influenced by AITC. It was found that AITC could form a hydrophobic region with COXⅡ protein via molecular docking, besides, a sulfur atom of AITC structure could form a length of 2.9 Å hydrogen bond with Leu-31. These results will provide valuable information for elucidating the role of COXⅡ in Sitophilus zeamais responses to AITC, meanwhile, it will helpful to carry out a point mutation in AITC binding sites for the future research.

The properties of the annual, semiannual and triennial oscillations (AO, SAO and TO) in the middle atmosphere have been investigated using the TIMED/SABER temperature data. The Lomb-Scargle and wavelet spectra were used to determine the dominant oscillations in the background temperature field. The AO is prominent at the mid-latitudes. The AO amplitudes present an asymmetry between the two Hemispheres, being larger in the mesosphere than in the stratosphere. The SAO dominates the tropical regions, with three amplitude maxima at altitudes of 45, 75, and 85 km. The SAOs in the upper mesosphere (75 km) are out of phase with those in the mesopause (85 km) in the tropical regions, which can generate an enhancement of 11 K at each equinox, contributing to the lower mesospheric inversion layer. The TO is significant in the tropical region, with amplitude being maximum at 35, 45 and 85 km. Result shows that there may be potential interaction by the TO with SAO at 85km at the equator. The relation between ENSO and TO has also been discussed. The ENSO signal may modulate the amplitude of the TO, mainly in the lower stratosphere. The real origin of the TO may lie in the wave-mean-flow interaction.

As the world population grows, fulfilling the need for biomaterials in the healthcare system becomes increasingly important. Biomaterials, which include metals, polymers, ceramics, and composites, play an important role in the creation of medical devices that improve people's lives. The European Society for Biomaterials described biomaterials as non-biological materials used in medical devices to interact with biological systems. This definition has developed to encompass materials that treat, assess, or replace tissues or bodily functions. Biocompatibility, as defined by the FDA, is a key feature of biomaterials, as is the requirement to fulfil design requirements such as mechanical performance, geometry, and electrical control. Over the last decade, advances in regenerative medicine and tissue engineering have boosted biomaterials' usage in medical applications dramatically. Despite its promise, scientists, engineers, and physicians continue to face significant challenges due to the complexity of biomaterials. Biomaterials have various benefits, including biodegradability, non-toxicity, and biocompatibility, making them extremely useful for replacing, sustaining, or improving biological activities in damaged tissues. They are used in a wide range of applications, including tissue engineering implants, human tissue healing and regeneration, medication delivery systems, and biosensors. This study gives insights into the fundamental characteristics, case studies, and ethical issues associated with the usage and use of biomaterials, further examining their potential and significance in healthcare and medicine.

The paper describes the new method for image compression based on coordinated group signal transformation. The algorithm is a type of difference coding. Coordinated processing significantly simplifies the difference signal conversion scheme using a single group codec for all signals. The described method considers color channels as correlated signals of a multi-channel communication system. The specifics of the processed data required modification of the coordinated group processing algorithm. First, we changed how to calculate the difference signals to prevent data loss. Secondly, the group codec was supplemented with a neural network to improve the quality of reconstructed images. We considered the following types of neural networks: fully connected, recurrent, convolution, and convolution in the Fourier space. Based on the simulation results, it is best to use fully connected neural networks if the goal is to minimize processing delay time. These networks have a response time of 13 ms. On the other hand, if the priority is to improve quality in cases where delays are not critical, then convolution neural networks in the Fourier space should be used. These networks have a response time of 140 ms and are of significant interest.

In electromagnetic ultrasonic testing, it is difficult to recognize small-size bottom cracks by time of flight (ToF), and the lift-off fluctuation of the probe affects the accuracy and consistency of the inspection results. In order to overcome the difficulty, a novel EMAT (electromagnetic acoustic transducer)-PEC (pulse eddy current) composite sensor is designed. We use amplitude of bottom echo recorded by EMAT to identify the tiny bottom crack as well as the amplitude of PEC signals picked up by the integrated symmetric coils to measure the average lift-off of the probe in real time. Firstly, the effects of lift-off and bottom cracks on amplitude of bottom echo are distinguished combining the theoretical analysis and finite element method (FEM). And then an amplitude correction method based on the fusion of EMAT and PEC signals is proposed to reduce the impact of lift-off on the defect signal. The experimental results demonstrate that the designed composite sensor can effectively detect the bottom crack as small as 0.1mm* 0.3mm. The signal fusion method can accurately correct the amplitude of defect signal and the relative error is less than ±8%.

The studied solar pot is a recent invention, which gained a utility model protection in 2021 from the Hungarian Intellectual Property Office under patent number 5489. The device is made for environmentally friendly cooking or heating (by utilizing solar energy) of foods and liquids. Its structure is similar to a double pipe heat exchanger, it has an outer mantle and an inner cooking tank. The goals of the paper are proposing a new physically-based mathematical model describing the solar pot and carrying out computer experiments with it, assembling an experimental system of the pot connected with a solar collector and performing measurements on it. Based on the results, the solar pot can successfully be used for cooking or sterilizing foods or liquids during the studied time period, in Hungary.

The research reported on this paper was aimed at improving the overall efficiency of a PDO certified artisanal cheese production process. Being a PDO certified foodstuff by the EU, it is considered to have properties and qualities determined by the geographical environment in which is made, with its production taking place in a specific and determined geographical location, in this case the Serra da Estrela region. In that sense, the authors conducted a mapping according to a systemic perspective of the processes involved in the context of manufacturing and distribution of certified Serra da Estrela cheese. Numerous methods were used throughout the process, such as a systemic design analysis, and techniques derived from ethnographic methods, which led to the collection of data in the field and consequently provided the immersion of the researcher in genuine work situations. Critical points were identified and emphasized in the systemic map with the purpose of encouraging initiatives to address and overcome the gaps and inefficiencies detected. The systemic design analysis triggered the development of design work. Observations following an ethnographic approach identified ergonomic risks in cheese making during the process of cutting excess chips, fostering the emergence of musculoskeletal disorders at the wrist. A tool that fits best to the task at hand was developed. A prototype of the new tool enabled collecting feedback from use in the work context, in order to inform product development. The domains of agricultural production and microbiology, considering the specific microorganisms developed trough the ripening process of the cheese, turned out to be aspects of high importance for the issue under focus, contributing to a broader understanding of the ripening process and its risks, simultaneously improving the efficiency and success of cheese production. If it were not for the systemic analysis, which served as a link between the boundaries of distinct domains such as the risk of microorganism contamination, ergonomics, energy efficiency, legislation and regulation policies, transportation challenges and economic viability, approached throughout the research. Simultaneously creating bridges between them, the various problems might not have been detected in the first place, as they are usually addressed in specialized disciplines, predetermined by the restrictions of each specific area of knowledge. As a consequence of the development of this research, which was based on an analysis that sought to establish possible connections between various disciplines and tried to constantly maintain a holistic perspective, making new connections and observing the issues from a new angle, apart from the already established methodologies. All this allowed to lay out the seeds for the development of a plan to tackle the critical points identified by the systemic analysis reported in this paper.

Abstract: Transcription factors are crucial pre-transcriptional regulatory mechanisms that can modulate the expression of downstream genes by binding to their promoter regions. DOF (DNA binding with One Finger) proteins are a unique class of transcription factors with extensive roles in plant growth and development. Our previous research indicated a decrease in iron content in chlorotic bamboo leaves. However, to our knowledge, genes related to iron metabolism pathways in bamboo species have not yet been studied. Therefore, in the current study, we identified iron metabolism-related (IMR) genes in bamboo and determined the transcription factors that significantly influence them. Among these, DOFs were found to have widespread effects and potentially significant impacts on their expression. We identified specific DOF members in Dendrocalamus latiflorus with binding abilities through homology with Arabidopsis DOF proteins, and established connections between some of these members and IMR genes using RNA-seq data. Additionally, molecular docking confirmed the binding interactions between these DlDOFs and the DOF binding sites in the promoter regions of IMR genes. The co-expression relationship between the two gene sets was further validated using q-PCR experiments. This study paves the way for research into iron metabolism pathways in bamboo and lays the foundation for understanding the role of DOF transcription factors in D. latiflorus.

This paper is focused on typical rural settlements in the Stara Planina Mountain area in Serbia. They are distinguished by their authenticity, identity and character, and they have still not been destroyed by inappropriate development as is the case in some other mountain areas in Serbia, where the effects of urbanization, globalization and homogenization are obvious. Consequently, there is a need to prevent these effects in mountain areas where there is a threat of disbalance between development and the inherited natural and cultural values. The paper starts from several important concepts that relate contemporary approaches to cultural heritage preservation, place morphology and planning future development. The concept definitions from recent documents from related fields are used. These concepts are then applied to the area of Stara Planina Mountain and its rural settlements. The necessity for an integrative approach to planning this area with significant natural and anthropogenic potential is pointed out, including its integration into international programs of sustainable development.

The wetlands in northeastern Bangladesh are home to some of the most prolific and valuable ecosystems on the planet, offering a wide range of benefits to both the local and wider communities. A limited number of research on this topic have been carried out in various wetlands in coastal hilsa, but none have been located in the northeastern region of Bangladesh. Thus, the goal of this study was to better understand the most commercially relevant species (anadromous hilsa) in northeastern Bangladesh as well as to assess the wetland ecosystem services more thoroughly with the contribution of their fish genetic resources. In addition to laboratory studies, fieldwork was done in the fishing settlements along the Surma River, Hakaluki Haor, and Tanguar Haor. The study classified 77 fish species into 21 subcategories of ecosystem services, of which 56% were not threatened, 17% were vulnerable, and 10% were highly endangered. The species Hilsa was found to be the most economically significant, accounting for 1% of the GDP overall. The study determined if the hilsa stock of the examined wetlands maintains a single or several subpopulations in comparison to other parts of the country when they migrate from saline water to northeastern Bangladesh (freshwater). But when compared to other groups, the FST score was between 0.000 to 0.017, indicating that the populations are identical and that there is genetic material sharing between them. Additionally, these statistics imply that the Sylhet haor and adjacent river systems contain a single stock of Hilsa fish. Nevertheless, a number of stresses and risks, including overexploitation, illicit and destructive fishing, siltation, and natural disasters like flash floods, have been linked to changes in the supply of hilsa and other ecosystem services. This study also emphasizes the necessity of policy attention and research to address the concerns.

Severe acute respiratory syndrome coronavirus type 2 (SARS-CoV-2) continues to be a global threat due to its ability to evolve and generate new subvariants, leading to new waves of infection. Additionally, other coronaviruses like Middle East respiratory syndrome coronavirus (MERS-CoV, formerly known as hCoV-EMC) which first emerged in 2012, persists and continues to present a threat of severe illness to humans. The continued identification of novel coronaviruses, coupled with the potential for genetic recombination between different strains, raises the possibility of new coronavirus clades of global concern emerging. As a result, there is a pressing need for pan-CoV therapeutic drugs and vaccines. After extensive optimization of an HCV protease inhibitor screening hit, a novel 3CLPro inhibitor (MK-7845) was discovered and subsequently profiled. MK-7845 exhibited nanomolar in vitro potency with broad spectrum activity against a panel of clinical SARS-CoV-2 subvariants and MERS-CoV. Furthermore, when administered orally, MK-7845 demonstrated a notable reduction of viral burdens by &gt;6 log orders in the lungs of transgenic mice infected with SARS-CoV-2 (K18-hACE2 mice) and MERS-CoV (K18-hDDP4 mice).

The continuous casting process of helical fiber reinforced metal matrix composites was proposed, and the experimental equipment was designed and manufactured. The relationship model be-tween the process parameters and the helical shape of the fibers in the metal matrix is analyzed by differential geometry. Helical carbon fiber reinforced lead matrix composites were prepared under different conditions. When the melting temperature and cooling intensity were increased, the helical radius of helical carbon fiber in lead matrix was increased. When the fiber rotation speed was increased, the helical radius was decreased, and the helical pitch was de-creased proportionally. The experimental results are consistent with the process model. Carbon fiber rein-forced aluminum composites were prepared. Scanning electron microscopy showed that the infiltration between the aluminum matrix and the carbon fiber was not complete. As the volume fraction of carbon fiber which was added in composites is too small, the mechanical properties of the composites have not been significantly improved.

This article presents an innovative approach to the design of a safe adaptive backstepping control system. Tailored specifically for underactuated marine robots, the system utilizes simple sensors for enhanced practicality and efficiency. Given their operation in diverse oceanic environments fraught with various sources of uncertainties, ensuring the system's safe and robust behavior holds paramount importance in the control literature. To address this concern, this paper introduces a control strategy designed to ensure robustness at both the kinematic and dynamic levels. By emphasizing the compensation for the system uncertainties, the design integrates a straightforward fuzzy system structure. To further ensure the system's safety, a funnel surface is defined, followed by the design of a suitable nonlinear sliding surface as a function of the funnel and tracking error. Specifically leveraging the Lyapunov function, the study formally establishes the Semi-globally Practically Finite-time Stability of the closed-loop system, validated through simulations conducted on underactuated marine robots.

Several types of guided bone regeneration materials are available with various properties and clinical indications. Among them, dentin-derived matrix from extracted teeth is an excellent alternative to traditional graft materials, such as allografts and xenografts. Different clinical preparation protocols exist: block form versus powder form, demineralized versus non-demineralized form. Out of these methods, demineralization protocols for dentin-derived matrix from extracted teeth have been noted for a wide range of successful clinical outcomes. The purpose of this animal study was to find out the most effective method of demineralizing dentin-derived matrix to result in the highest regenerative ability in the bone graft material in rabbit calvaria. The study conducted a comparative histomorphometric analysis of four groups in distinguished matrix conditions: a control group without graft placement, a non-demineralized dentin-derived matrix graft placement group, a 15-minute demineralized dentin-derived matrix graft placement group, and a 30-minute demineralized dentin-derived matrix graft placement group. Regenerative processes were evaluated three times at 2, 4, and 8 weeks post-graft placement. These groups of rabbits were evaluated randomly in a blinded setting to prevent bias. Among the four groups compared, the group with a 15-minute demineralized dentin-derived matrix graft showed the most efficient bone regeneration in the histomorphometric analysis. Based on this animal study, it was apparent that a 15-minute demineralization of dentin-derived matrix is the preferred preparation protocol to maximize the regenerative potential in the matrix.

Promoting green development has become an important way to optimize the ecological and economic structure and promote sustainable development. The Yangtze River Economic Belt is an important economic corridor in China, and it remains to be examined whether the implementation of environmental regulations has enhanced the green total factor productivity (GTFP) of cities. This paper calculates the green total factor productivity of 107 cities within the Yangtze River Economic Belt by using the super-efficient SBM model and the GML index with Chinese city panel data from 2007-2019 and measures the intensity of environmental regulations through textual analysis. The bidirectional fixed-effects model constructed in this paper suggests an inverted U-shaped relationship between environmental regulation and GTFP, which is confirmed by a series of robustness tests. Green technology innovation and advanced industrial structure play a mechanism role in this. In regions with lower levels of green technology and industrial structure, the inverted U-shaped relationship between environmental regulation and green total factor productivity is more significant. In addition, the phenomenon of GTFP rising and then falling because of environmental regulation is more obvious in cities in the middle and upper reaches of the Yangtze River and outside the urban agglomerations. Therefore, when formulating environmental regulation policies, it is necessary to balance the relationship between economic development and environmental protection and harmonize the environment and economic development of the entire Yangtze River Basin.

The main purpose of this study is the determination of the optimal data acquisition and processing parameters of electric and seismic tomographic techniques, for the investigation of complex geological environments. Two different study areas, in central-east Peloponnese and SW Attica were selected, where a detailed geological mapping and surface geophysical survey were carried out. The applied geophysical survey included the application of electrical resistivity tomography (ERT) and seismic refraction tomography (SRT). The geoelectrical measurements were acquired with different arrays and electrode configurations. Moreover, various types of seismic sources were used at seventeen shot locations along the seismic arrays. For the processing of geoelectrical data, clustered datasets were created increasing the depth of investigation and the discriminatory capability. The seismic data processing included: (a) creation of synthetic models and seismic records to determine the effectiveness and capabilities of the technique, (b) spectral analysis of the seismic records to determine the optimal seismic source type and (c) inversion of the field data to create representative subsurface velocity models. The results of the two techniques successfully delineated the complex subsurface structure that characterizes these two geological environments. The application of the ERT combined with the SRT, are the two dominant, high-resolution techniques for the elucidation of complex subsurface structures.