Interval-valued functions have been widely used to accommodate data inexactness in optimization and decision theory. In this paper, we study interval-valued vector optimization problems, and derive their relationships to interval variational inequality problems, of both Stampacchia and Minty types. Using the concept of interval approximate convexity, we establish necessary and sufficient optimality conditions for local strong quasi and approximate $LU$-efficient solutions to nonsmooth optimization problems with interval-valued multiobjective functions.

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

This article develops applications of the generalized method of lines to numerical solutions of the time-independent, incompressible Navier-Stokes system in fluid mechanics. We recall that for such a method, the domain of the partial differential equation in question is discretized in lines (or more generally in curves), and the concerning solutions are written on these lines as functions of the boundary conditions and the domain boundary shape.

This article explores the relationship between convex functions defined on integers ($\mathbb{Z}$) and their extension to real numbers ($\mathbb{R}$). We introduce key definitions and investigate the hypothesis that there exists a unique convex curve within this family of functions, leading to a proof by contradiction. Our findings highlight the preservation of convexity as functions transition from integers to real numbers.

In this paper, we consider a class of bilevel programming problems (abbreviated as, BLPP). Exploiting the generalized approximate convexity assumptions, we investigate the relations among the solutions of approximate Minty (respectively, Stampacchia) type variational inequalities (abbreviated as, AMTVI (respectively, ASTVI)), and the local ϵ-quasi solutions of the BLPP. Moreover, by employing the generalized Knaster–Kuratowski–Mazurkiewicz (abbreviated as, KKM)-Fan’s lemma, we derive some existence results for the solutions of approximate variational inequalities (abbreviated as, AVI), namely, AMTVI and ASTVI. A non-trivial example is given to highlight the importance of the established results. To the best of our knowledge, there is no research paper available in the literature that establishes relationships between the AVI and the BLPP under the assumptions of generalized approximate convexity in terms of limiting subdifferentials.

In this work, we introduce the class of h-MN-convex functions by generalizing the concept of MN-convexity and combining it with h-convexity. Namely, let M : [0, 1] → [a, b] be a Mean function given by M (t) = M (t; a, b); where by M (t; a, b) we mean one of the following functions: A_t (a, b) := (1 − t) a + tb, G_t (a, b) = a^1−tb^t and H_t (a, b) := $\frac{ab}{ta+\left(1-t\right)b}=\frac{1}{A_t\left(\frac{1}{a},\frac{1}{b}\right)}$ with the property that M (0; a, b) = a and M (1; a, b) = b. Let I, J be two intervals subset of (0, ∞) such that (0, 1) ⊆ J and [a, b] ⊆ I. Consider a non-negative function h : J → (0, ∞), a function f : I → (0, ∞) is said to be h-MN-convex (concave) if the inequality f (M (t; x, y)) ≤ (≥) N (h(t); f (x), f (y)), holds for all x, y ∈ I and t ∈ [0, 1]. In this way, nine classes of h-MN-convex functions are established, and therefore some analytic properties for each class of functions are explored and investigated. Characterizations of each type are given. Various Jensen’s type inequalities and their converses are proved.

In this paper, some convexity properties and some inequalities for the (p,k)-analogue of the Gamma function, Г_p,k(x) are given. In particular, a (p,k)-analogue of the celebrated Bohr-Mollerup theorem is given. Furthermore, a (p,k)-analogue of the Riemann zeta function, ζ_p,k(x) is introduced and some associated inequalities are derived. The established results provide the (p,k)-generalizations of some known results concerning the classical Gamma function.

Causality is the most important topic in the history of Western Science, and since the beginning of the statistical paradigm, it meaning has been reconceptualized many times. Causality entered into the realm of multi-causal and statistical scenarios some centuries ago. Despite of widespread critics, today Deep Learning and Machine Learning advances are not weakening causality but are creating a new way of finding indirect factors correlations. This process makes possible us to talk about approximate causality, as well as about a situated causality.

This report discusses the application of approximate dynamic programming (ADP) and Krylov subspace methods in solving sequential decision-making problems in machine learning. ADP is used when dealing with large state spaces or when the exact dynamics are unknown. The paper explores various ADP methods such as temporal difference learning and least-squares policy evaluation. The authors also focus on the use of Krylov subspace methods for solving the Bellman equation in ADP. The report provides insights into linear approximation, stochastic algorithms, and the Arnoldi algorithm for orthonormal basis. Overall, the paper highlights the theoretical foundation provided by ADP and its connection with Krylov subspace methods, shedding light on their application in computer science.

We analyze the modular geometry of the variable exponent Lebesgue space L^p(.). We show that L^p(.) possesses a modular uniform convexity property. Part of the novelty is that the property holds even in the case supp(x) = ∞ . We present specific applications to fixed point theory. xÆΩ

We introduce the notion of generalized contraction on dualistic partial metric spaces. A fixed point theorem for mappings satisfying above mentioned contraction is obtained. Some consequences of our result are obtained. We construct an example to demonstrate the effectiveness of our result among the corresponding results in partial metric spaces. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. We discuss an application of our fixed point results to show the existence of solution of functional equations.

A single-crystal of ytterbium-doped “mixed” yttrium-lutetium aluminium garnet with a stoichiometric composition of (Y0.601Lu0.233Yb0.166)3Al5O12 was grown by the Czochralski method and its structure, vibronic, spectroscopic and laser properties were studied. The stimulated-emission cross-section for Yb3+ ions was maximized to 2.53×10-20 cm2 at 1031 nm, the emission bandwidth is ~8 nm and the reabsorption-free luminescence lifetime of the 2F5/2 state is 1.063 ms. Pumped at 941 nm, the Yb-laser generated a maximum output power of 1.04 W at 1.03 and 1.05 μm with a high slope efficiency of 76.4% and a laser threshold of 76 mW. A continuous wavelength tuning over a range of 51.6 nm (1026.4 - 1078.0 nm) was also achieved. Power scaling is achieved using a 969 nm-diode pumped microchip cavity. A maximum output power of ~9 W is obtained at 1.05 μm with a slope efficiency of 76% and with an almost circular laser beam profile.

Drowsiness is a main factor for various costly defects, even fatal accidents in areas such as construction, transportation, industry and medicine, due to the lack of monitoring vigilance in the mentioned areas. The implementation of a drowsiness detection system can greatly help to reduce the defects and accident rates by alerting individuals when they enter a drowsy state. This research proposes an Electroencephalography (EEG) based approach for detecting drowsiness. EEG signals are passed through a preprocessing chain composed of artifact removal and segmentation to ensure accurate detection followed by different feature extraction methods to extract the different features related to drowsiness. This work explores the use of various machine learning algorithms such as Support Vector Machine (SVM) the K Nearest Neighbor (KNN) the Naive Bayes (NB) the Decision Tree (DT) and the Multilayer Perceptron (MLP) to analyze EEG signals sourced from the DROZY database, carefully labeled into two distinct states of alertness (awake, and drowsy). Segmentation into 10-second intervals ensures precise detection, while a relevant feature selection layer enhances accuracy and generalizability. The proposed approach achieves high accuracy rates of 99.84% and 96.4% for intra (subject by subject) and inter (cross-subject) modes, respectively. SVM emerges as the most effective model for drowsiness detection in the intra mode, while MLP demonstrates superior accuracy in the inter mode. This research offers a promising avenue for implementing proactive drowsiness detection systems to enhance occupational safety across various industries.

We investigate the existence and representation of the generalized core-EP inverse of some triangular matrices over a Banach algebra. Further, the general representations of the generalized core-EP inverse of a triangular matrix over a $C^*$-algebra are presented. As applications, the generalized core-EP inverses of some block operator matrices over Hilbert spaces are given.

It has been empirically observed that the upper tail of the firm size distribution follows either the Pareto distribution or the Zipf distribution, with both patterns being explained by Gibrat’s law (Gabaix, 1999). This article analyzed firm revenue data from China, spanning from 2005 to 2013, to examine the whole range of the firm size distribution. Our empirical analysis revealed that firm revenue data over these years is well fitted by a three-parameter generalized Pareto distribution, with the fitted parameters indicating a dichotomy: The size distribution of large-sized firms, namely the upper tail, is asymptotically characterized by a Pareto distribution or a Zipf distribution, whereas the size distribution of smaller and medium-sized firms is approximated by an exponential distribution. This finding suggests that Gibrat’s law should be extended to account for the emergence of a generalized Pareto distribution.

In this paper, we present Binet's formulas, generating functions, and the summation formulas for generalized Pentanacci numbers, and as special cases, we investigate Pentanacci and Pentanacci-Lucas numbers with their properties. Also, we define Gaussian generalized Pentanacci numbers and as special cases, we investigate Gaussian Pentanacci and Gaussian Pentanacci-Lucas numbers with their properties. Moreover, we give some identities for these numbers. Furthermore, we present matrix formulations of generalized Pentanacci numbers and Gaussian generalized Pentanacci numbers.

We introduce a new generalized inverse which is a natural generalization of (pseudo) right core inverse in a Banach *-algebra. We characterize this generalized inverse by using right core and quasi-nilpotent decomposition. We then present its polar-like characterization and investigate related algebraic properties. Finally, the right core-EP inverse is characterized by certain new ways.

In this paper we use Toeplitz quantization to extend in a very natural way Kostant's theorem for the group $SU(m)$ to the group of symplectomorphisms of the unit sphere and we also give another proof of the infinite dimensional version of Schur and Horn theorem for the sphere based on Schur and Horn theorem for Hermitian matrices.

Let $(\{f_j\}_{j=1}^n, \{\tau_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^n, \{\omega_k\}_{k=1}^n)$ be two p-orthonormal bases for a finite dimensional Banach space $\mathcal{X}$. If $ x \in \mathcal{X}\setminus\{0\}$ is such that $\theta_fx$ is $\varepsilon$-supported on $M\subseteq \{1,\dots, n\}$ w.r.t. p-norm and $\theta_gx$ is $\delta$-supported on $N\subseteq \{1,\dots, n\}$ w.r.t. p-norm, then we show that \begin{align}\label{ME} &o(M)^\frac{1}{p}o(N)^\frac{1}{q}\geq \frac{1}{\displaystyle \max_{1\leq j,k\leq n}|f_j(\omega_k) |}\max \{1-\varepsilon-\delta, 0\},\\ &o(M)^\frac{1}{q}o(N)^\frac{1}{p}\geq \frac{1}{\displaystyle \max_{1\leq j,k\leq n}|g_k(\tau_j) |}\max \{1-\varepsilon-\delta, 0\},\label{ME2} \end{align} where \begin{align*} \theta_f: \mathcal{X} \ni x \mapsto (f_j(x) )_{j=1}^n \in \ell^p([n]); \quad \theta_g: \mathcal{X} \ni x \mapsto (g_k(x) )_{k=1}^n \in \ell^p([n]) \end{align*} and $q$ is the conjugate index of $p$. We call Inequalities (\ref{ME}) and (\ref{ME2}) as \textbf{Functional Donoho-Stark Approximate Support Uncertainty Principle}. Inequalities (\ref{ME}) and (\ref{ME2}) improve the finite approximate support uncertainty principle obtained by Donoho and Stark \textit{[SIAM J. Appl. Math., 1989]}.

This paper introduces a novel 3D NoC router that combines buffered and bufferless routing with approximate priority comparison when deflecting flits. Our proposal is a modification of an asymmetrical router that is buffered in the z dimension ports and bufferless in the x and y dimension ports. Flits that request output ports in the x and y dimensions are granted or deflected based on approximate, instead of accurate, priority comparison. Experimental results show that the proposed router, besides effectively combining the advantages of both buffered and bufferless routers, it achieves additional performance and area gains due to the reduced logic required for approximate priority comparison in flit deflections. Experimental results using synthetic and realistic traffic show that the proposed router begins to saturate at a sifnificantly higher injection rate than a bufferless router, but at a slightly lower injection rate than when using accurate priority comparison. Furthermore, the proposed router achieves higher clock frequencies and reduced area compared to the simpler permutation network.

A new generalized definition of Mersenne numbers is proposed of the form (a^n - (a-1)^n), called Global Generalized Mersenne numbers, or simply Generalized Mersenne numbers and noted GM_{a,n} where a is the base and n is the exponent, both being positive integers. The properties are investigated for prime exponents n and several theorems on Mersenne numbers regarding their congruence properties are generalized and demonstrated. In particular, it is found that, for any base a, Generalized Mersenne numbers are in general such that (GM_{a,n} - 1) are even and divisible by n, a and (a-1) for any odd prime exponent n and by (a(a-1)+1) for any prime exponent n > 5. The remaining factor is a function of triangular numbers of (a-1), specific to each prime exponent n. Four theorems on Mersenne numbers are generalized and four new theorems are demonstrated, allowing to show first, that (GM_{a,n} - 1) are divisible by 6, and more precisely GM_{a,n} are congruent to 1(mod 12) or 7(mod 12) depending on the congruence of the base a(mod 4); second, that (GM_{a,n} - 1) are divisible by 10 if n == 1(mod 4) and, if n == 3(mod 4), GM_{a,n} == 1(mod 10), or 7(mod 10) or 9(mod 10) depending on the congruence of the base a(mod 5); third, that all factors c_{i} of GM_{a,n} are of the form (2nf_{i}+1) with f_{i} natural integers such that c_{i} is prime itself or the product of primes of the form (2nj+1) with j natural integer; fourth, that for odd prime exponents n, all GM_{a,n} are periodically congruent to either +/-1\(mod 8) or +/-3(mod 8) depending on the congruence of the base a(mod 8); and fifth, that the factors of a composite GM_{a,n} is of the form (2nf_{i}+1) with f_{i} == u(mod 4) and u being either 0, 1, 2 or 3 depending on the congruence of the exponent n(mod 4) and on the congruence of the base a(mod 8). The potential use of Generalized Mersenne primes in cryptography is shortly addressed.

In this paper, we introduce the notion of the generalized $w$-group inverse in a Banach algebra with proper involution. This is a natural generalization of generalized (weak) group inverse in Banach *-algebras. Many elementary properties of such new weighted generalized inverse are presented. We further establish the equivalent relations between generalized weighted group inverse and weighted generalized Drazin inverse. Related properties of generalized (weak) group inverse are extended to the wider cases.

Dual generalized commutative quaternions have broad application prospects in many fields. Additionally, the matrix equation AXB = C has important applications in mathematics and engineering, especially in control systems, economics, computer science, and other disciplines. However, research on the matrix equation AXB = C over the dual generalized commutative quaternions remains relatively insufficient. In this paper, we derive the necessary and sufficient conditions for the solvability of the dual generalized commutative quaternion matrix equation AXB = C. Furthermore, we provide the general solution expression for this matrix equation, when it is solvable. Finally, a numerical algorithm and an example are provided to confirm the reliability of the main conclusions.

Microgrid (MG) control is essential for efficient, reliable, and sustainable energy management in distributed energy systems. Genetic Algorithm-based energy management systems (GA-EMS) can optimally control a MG by finding global optima and handling complex, non-linear, and non-convex problems, but they can be computationally intensive, making real-time control challenging. Model Predictive Control (MPC)-based EMS predicts future behaviour over a defined horizon, ensuring optimal performance and constraint satisfaction but typically relies on linear models. This paper proposes a novel Genetic Predictive Control (GPC) method, combining GA and MPC to enhance resource allocation, balance multiple objectives, and adapt dynamically to changing conditions. Integrating GA with MPC significantly improves the handling of non-linearities and non-convexity in the system model, leading to more accurate and effective control. Comparative analysis shows that GPC significantly reduces excess power production—surplus power generated beyond load demand—improving resource allocation efficiency. For instance, in the Mutation–Random Selection scenario, GPC reduced excess power to 76.0W compared to 87.0W with GA. Additionally, GPC balances cost, emissions, and power efficiency. In the Crossover-Elitism scenario, GPC achieved a daily cost of $113.94 compared to GA's $127.80, and carbon emissions of 52.83 kg CO2e compared to GA's 69.71 kg CO2e, demonstrating GPC's cost efficiency and environmental benefits. While MPC optimizes a weighted sum of objectives, designing appropriate weights can be challenging and may result in non-convex problems. GA handles multiple, conflicting objectives through multi-objective optimization, providing Pareto-optimal solutions. GPC's dynamic adaptability maintains optimal performance by forecasting future load demands and adjusting control actions. GPC consistently achieves lower emissions than GA across various scenarios and, although it sometimes incurs higher costs, such as $113.94 compared to $131.90 in the Crossover–Random Selection scenario, its holistic approach balances these costs with other metrics, making it cost-effective in the long run. By reducing excess power production and emissions, GPC contributes to economic savings and promotes sustainable practices. These findings underscore GPC's potential as a versatile, efficient, and environmentally beneficial optimization tool for power generation systems.

To determine the photon emission or absorption probability for a diatomic system in the context of the semiclassical approximation it is necessary to calculate the characteristic canonical oscillatory integral which has one or more saddle points. Integrals like that appear in a whole range of physical problems, e.g. the atom-atom and atom-surface scattering and various optical phenomena. A uniform approximation of the integral, based on the stationary phase method is proposed, where the integral with several saddle points is replaced by a sum of integrals each having only one or at most two real saddle points and is easily soluble. In this way we formally reduce the codimension in canonical integrals of "elementary catastrophes" with codimensions greater than 1. The validity of the proposed method was tested on examples of integrals with three saddle points ("cusp" catastrophe) and four saddle points ("swallow-tail" catastrophe).

In this paper, we introduce and investigate a new family of sequences called the generalized Fibospinomials (or the generalized Fibonacci polynomial spinors or Horadam polynomial spinors). Being particular cases, we handle with $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomial spinors. After a short history on spinors and quaternions, we present Binet's formulas, generating functions and the summation formulas for these polynomials. In addition, we obtain some identities of generalized Fibonacci polynomial spinors, $(r,s)$-Fibonacci polynomial spinors and $(r,s)$-Lucas polynomial spinors. Moreover, we give some special identities such as Catalan's and Cassini's identities and we present matrices related with these polynomials.

Motivated by empirical observations, we propose a possible extension of Gibrat's law. By applying it into the random growth theory of income distribution (Gabaix, 2009), we find that the income distribution is described by a generalized Pareto-type distribution (GPD) with three parameters. We observe that there is a parameter /elta in the GPD that plays a key role in determining the shape of income distribution. By using the Kolmogorov-Smirnov test, we empirically show that, for typical market-economy countries, /elta is close to 0 significantly, such that the income distribution is characterized by a two-class pattern in which the bottom 90% of the population is approximated by an exponential distribution and the richest 1%~3% is approximated by an asymptotic power law. However, we empirically find that, for China both in planned economy period and in early stages of market reformation (from 1978 to 1990), /elta is significantly deviated from 0, such that the bottom of the population no longer conforms to an exponential distribution.

This paper presents machine learning methods for approximate solutions of reaction-diffusion equations with multivalued interaction functions. This approach addresses the challenge of finding all possible solutions for such equations, which often lack uniqueness. The proposed method utilizes physics-informed neural networks (PINNs) to approximate generalized solutions.

We approximate the trigonometric function sine and cosine on the interval . This analysis provides two formulas to approximate sine and cosine. At first, we try to derive the formula which involves a square root, and then we derive another formula that does not require any use of a square root. Nevertheless, after deriving the procedure which requires no square root, we further try to increase its accuracy and then derive another formula that approximates trigonometric functions more accurately on the interval [0, pi/2]. So, this analysis provides mainly two types of procedures. One uses square roots, whereas the other does not. We also focus on ensuring the accuracy of these trigonometric functions in the interval [0,pi/2]. This accuracy analysis is portrayed using the graph. This graph shows the difference between the values generated by the functions defined here and the actual value of these functions. So, these graphs also indicate the error of these functions on that interval. Finally, we compare our approximation with the approximation formula of the 7th-century Indian Mathematician Bhaskara I.

In this work, an innovative numerical approach for polylinear approximation (polylinearization) of non-self-intersecting compact sensor characteristics (transfer functions) specified either pointwise or analytically is introduced. The goal is to optimally partition the sensor characteristic, i.e. to select the vertices of the approximating polyline (approximant) along with their positions on, the sensor characteristics so that the distance (i.e. the separation) between the approximant and the characteristic is rendered below a certain problem-specific tolerance. To achieve this goal, two alternative non-linear optimization problems are solved, whose essential difference is in the adopted quantitative measure of the separation between the transfer function and the approximant. In the first problem, which relates to absolutely integrable sensor characteristics (their energy is not necessarily finite, but they can be represented in terms of convergent Fourier series), the polylinearization is constructed by numerical minimization of the L^1--metric (a distance-based separation measure), concerning the number of polyline vertices and their locations. In the second problem which covers the quadratically integrable sensor characteristics (whose energy is finite, but they do not necessarily admit a representation in terms of convergent Fourier series), the polylinearization is constructed by minimizing numerically the L^2-metric (area-, or energy-based separation measure) for the same set of optimization variables –the locations, and the number of polyline vertices.

Transformation formula under the action of a general linear fractional transformation for generalized Dedekind eta-function has been a subject of intensive study, Rademacher, Dieter, Meyer et al. However, the (Hecke) modular relation structure has not been recognized until the work of Goldstein-de la Torre, and streamlining the classical proofs in the modular relation will reveal the meaning hidden in those works. Our main aim is to elucidate the works of these researchers in the context of modular relations.

We introduce and analyze conceptual approximations of the Boussinesq equation for horizontal unconfined aquifers during the pure drainage phase, without any reharge and zero-inflow conditions. We employ a variety of methods, which include wave solution, variable separation and series expansion to constract a new model and explore its behavior and performance against the Boussinesq equation and its exact (non-closed form) solution, at early and later times. The modeled non-linear forms are finally linearized concluding with explicit analytical expressions that incorporate most of the basic characteristics regarding the evolution of the water table and the outflow from the exact Boussinesq equation under different initial conditions. The endeavors of this work might be useful for theoretical and modeling purposes related to this problem.

We investigate some information properties of consecutive k-out-of-n:G systems in light of fractional generalized cumulative residual entropy. We firstly derive a formula to compute fractional generalized cumulative residual entropy related to the system's lifetime and explore its preservation properties in terms of established stochastic orders. Additionally, we obtain useful bounds. To aid practical applications, we propose two non parametric estimators for the fractional generalized cumulative residual entropy in these systems. The efficiency and performance of these estimators are illustrated using simulated and real datasets.

The radio spectrum is a scarce and extremely valuable resource that demands careful real-time monitoring and dynamic resource allocation. Dynamic spectrum access (DSA) is a new paradigm for managing the radio spectrum, which requires AI/ML driven algorithms for optimum performance under rapidly changing channel conditions and possible cyber-attacks in the electromagnetic domain. Fast sensing across multiple directions using array processors, with subsequent AI/ML based algorithms for sensing and perception of the waveforms that are measured from the environment is critical for providing decision support in DSA. As part of directional and wideband spectrum perception, the ability to finely channelize wideband inputs using efficient Fourier analysis is much needed. However, a fine-grain fast Fourier transform (FFT) across a large number of directions is computationally intensive and leads to high chip area and power consumption. We address this issue by exploiting recently proposed approximate discrete Fourier transforms (ADFT) which has its own sparse factorization for real-time implementation at low complexity and power consumption. The ADFT is used to create a wideband multi-beam RF digital beamformer and temporal spectrum-based attention unit which monitors 32~discrete directions across 32~sub-bands in real-time using a multiplierless algorithm having low computational complexity. The output of this spectral attention unit is applied as a decision variable to an intelligent receiver that adapts its center frequency and frequency resolution via FFT channelizers that are custom-built for real-time monitoring at high resolution. This two-step process allows the fine-gain FFT to be applied only to directions and bands of interest as determined by the ADFT based low-complexity 2D spacetime attention unit. The fine-grain FFT provides a spectral signature that can find future use cases in neural network engines for achieving modulation recognition, IoT device identification, and RFI identification. Beamforming and spectral channelization algorithms, digital computer architecture, and early prototypes using a 32-element fully digital multichannel receiver and field programmable gate array (FPGA)-based high-speed software defined radio (SDR) is provided.

In the study of rough sets, there are many covering approximation spaces, how to classify covering approximation spaces has become a hot issue. In this paper, we propose concepts covering approximation $T_{1}$-space, $F-$symmtry, covering rough continuous mapping, covering rough homeomorphism mapping to solve this question. We also propose a new method for constructing topology in Theorem 5.1, and get the following properties: (1) For each $x\in U$, $\{X_{i}:i\in I\}\subseteq \mathcal{P}(U)$ is all the subsets of $U$ which contains $x$ and $*$ is a reflexive relation on $U$. If $V\in \tau$ is a subset of $U$ and $x\in V$, then $\underline{*}(\bigcap \limits_{i\in I}X_{i})$ is the smallest subset of $U$ and $x \in \underline{*}(\bigcap \limits_{i\in I}X_{i})\subseteq V$. Denoted by $C(x)=\bigcap \{\underline{*}(X_{i}):x\in \underline{*}(X_{i}),i\in I\}$. (2)If $V\in \tau$ is a subset of $U$, then $V =$ $\bigcup \limits_{x\in V} C(x)$. (3) Let $\{\underline{*}(X_{i}):x\notin \underline{*}(X_{i}), i\in I\}$, then $\overline{\{x\}}$ $=$ $U \setminus \bigcup \limits_{x\notin \underline{*}(X_{i}), i\in I}\underline{*}(X_{i})$; (4) Let $*$ be a reflexive relation on $U$. For every $X\subseteq U$, we have $int(\underline{*}(X))=\underline{*}(X)$. Where $int(\underline{*}(X))$ represents the interior of $\underline{*}(X)$. (5) Let $\{\underline{*}(X_{i}):x\in \underline{*}(X_{i}),i\in I\}$ be a family subsets of $U$, then $\{\underline{*}(X_{i}):x\in \underline{*}(X_{i}),i\in I\}$ is a base for $(U,\tau)$ at the point $x$. \\

The most recent National Research Council Nutrient Requirements for Sheep and Goats was published in 2007, one of the most consequential nutrient requirement recommendations for sheep and goats in the world. It is pertinent to continue the refinement and discussion of nutrient utilization and requirements for the purposes of enhancing the efficiency of production systems, maximizing resource economy, and minimizing the carbon footprint, among others. Progress has been made in the estimation of energy and protein requirements in sheep and goats, mainly utilizing empirical feeding experimentation, comparative slaughter technique and minimum endogenous loss method. In sheep, newer estimates of energy and protein requirements for maintenance and growth and partial efficiencies had been reported since 2007. There were suggestions that energy and protein requirements could have been affected by breed, wool growth, gender and size; with these reported values being similar or lower than the recommended values in international feeding systems such as NRC, ARC, INRA and AFRC. In goats, energy and protein requirements for growing goats were reported to be either higher or lower than the established recommendations, depending upon meat or dairy breeds. Effect of gender on energy requirement appeared to be related to the stage of growth or degree of maturity. Newer data also suggested that the guidelines of the major feeding systems for the entire growth phase may not be adequate for non-pregnant and non-lactating pubertal females. In multiparous pregnant goats, energy and protein requirements for maintenance did not appear to be affected by days of pregnancy, but efficiencies of metabolizable energy and metabolizable protein utilization for pregnancy were. There were suggestions that that metabolizable protein synthesis in the rumen can be predicted from energy intake using combined equations that encompass both sheep and goats, but more data on goats were called for to account for specific differences in nutrition. In addition to sulfur, there has been progress made on the estimation of maintenance and growth requirements of calcium, phosphorus, potassium and magnesium in goats, with suggestions on the consideration of gender and breed differences. Species, level of Intake, genotype, mature size, age, gender, body composition, use of tissue energy, activity, season, and acclimatization continue to be important considerations for the estimation of nutrient requirements in sheep and goats, with emerging factors such as climate change, heat stress, parasitism and secondary plant compounds. Model equations and partial efficiencies used by NRC to predict energy and protein requirements for maintenance, growth, lactation, and fiber have been highlighted and discussed for the purpose of a more focus discussion and refinement for the future. Potential and limitation of both traditional and emerging methodologies in determining the nutrient requirements in sheep and goats were discussed. To justify the research investment, emerging methodologies such as nutrigenomics will have to be linked more directly to the improvement of production efficiency via more precise prediction of nutrient requirement.

Background: Anxiety disorders can be both an independent risk factor of many somatic conditions and the cause of complications of various organic disorders leading to poor prognosis. Objectives: The purpose of this study is to compare the heart rate variability (HRV) recorded both during the day and at night in patients with anxiety disorders and healthy individuals. Methods: The study was conducted on fifty consecutive outpatients with anxiety disorders who participated in intensive group psychotherapy. The diagnosis was made according to DSM-IV-TR criteria using the PSE-10 questionnaire. Out of 50 patients under study, 17 were diagnosed with panic disorder (PD) and 21 with generalized anxiety disorder (GAD). The control group consisted of 40 healthy people. The resulting three groups were compared in terms of circadian HRV using the Oxford Medilog Suprima Holter System. Results: The HRV analysis showed the nocturnal falls in the time and frequency parameters related to parasympathetic activity (rMSSD, pNN50, HF). The most unfavourable alterations were observed in the PD group, which comprised the disappearance of day vs. night amplitude of the majority of HRV parameters. Hence, the PD group was particularly susceptible to the arrhythmic events. It was noticeable that nocturnal vagotonia in the PD group was significantly lower as compared with the GAD and control group. Conclusions: The innovative aspect of the present study was to find a distinct profile of HRV with regard to the types of anxiety disorders because of the existing considerable differences between the nature of PD and GAD.

Soarinho Alkaline Intrusion, southeastern Brazil, makes part of the Serra do Mar Igneous Province, and it is composed of alkali feldspar syenite, alkali feldspar trachyte, quartz syenite, and mon-zonite. Geochemical and geochronological analysis of the Soarinho were compared with data from its neighbors Rio Bonito and Tanguá. Zircon U-Pb Laser Ablation ages show that Soarinho is youngest than Rio Bonito and Tanguá. Ages obtained from the monzonite (60 ± 2 Ma), alkali feldspar syenite (58 ± 2 Ma), and quartz syenite (58 ± 2 Ma) are indistinguishable within error. Petrographic and geochemical data show a clear contrast among Soarinho, Rio Bonito, Tanguá, and Lu-Hf isotopic data for the three alkaline intrusions (all negative), point to some similarities in their sources. The data suggest an enriched mantle source for Soarinho; however, an older con-tinental crust contribution cannot be discarded.

The Householder transformation, allowing a rewrite of probabilities into expectations of dichotomic observables, is generalized in terms of its spectral decomposition. Dichotomy is modulated by allowing more than one negative eigenvalues, or by abandoning it altogether, yielding generalized operator valued arguments for contextuality. We also discuss a form of state-dependent contextuality by variation of the functional relations of the operators; in particular, by additivity.

This study focuses on a new class of functions called sub-b-s-preinvex, that is a generalization of sub-b-s-convex and preinvex functions, and discusses some of their properties. A new sub-b-s-preinvex programming is introduced and the sufficient conditions of optimality under this type of function is established.

The fractional reduced differential transform method is a finite iterative method based on infinite fractional expansions. The result obtained is the approximation of the real value. There are few reports on the approximate error and the applicable condition. In this paper, according to the fractional expansions, we study the factors related to the approximate errors. Our research shows that the approximate errors relate not only to fractional order but also to time $t$ and increase rapidly with time $t$. This method can only be applied within a certain time range and the time range is relevant to fractional order and fractional expansions. Then, many obtained achievements may be incorrect if the applicable conditions are not satisfied. Some examples presented in this paper verify our analysis.

Linear mixed models are frequently used for analysing heterogeneous data in a broad range of applications. The restricted maximum likelihood method is often preferred to estimate co-variance parameters in such models due to its unbiased estimation of the underlying variance parameters. The restricted log-likelihood function involves log determinants of a complicated co-variance matrix. An efficient statistical estimate of the underlying model parameters and quantifying the accuracy of the estimation requires the first derivatives and the second derivatives of the restricted log-likelihood function, i.e., the observed information. Standard approaches to compute the observed information and its expectation, the Fisher information, is computationally prohibitive for linear mixed models with thousands random and fixed effects. Customized algorithms are of highly demand to keep mixed models analysis scalable for increasing high-throughput heterogeneous data sets. In this paper, we explore how to leverage an averaged information splitting technique and dedicate matrix transform to significantly reduce computations and to accelerate computing. Together with a fill-in reducing multi-frontal sparse direct solver, the averaged information splitting approach improves the performance of the computation process.

This work is devoted to physical vapor deposition synthesis, and characterisation of bismuth and lutetium-substituted ferrite-garnet thin-film materials for magneto-optic (MO) applications. The properties of garnet thin films sputtered using a target of nominal composition type Bi_0.9Lu_1.85Y_0.25Fe_4.0Ga₁O₁₂ are studied. By measuring the optical transmission spectra at room temperature, the optical constants and the accurate film thicknesses can be evaluated using Swanepoel’s envelope method. The refractive index data are found to be matching very closely to these derived from Cauchy’s dispersion formula for the entire spectral range between 300-2500 nm. The optical absorption coefficient and the extinction coefficient data are studied for both the as-deposited and annealed garnet thin-film samples. A new approach is applied for accurately deriving the optical constants data simultaneously with the physical layer thickness, using a combination approach employing custom-built spectrum-fitting software in conjunction with Swanepoel’s envelope method. MO properties, such as specific Faraday rotation, MO figure of merit and MO swing factor are also investigated for several annealed garnet-phase films.

In the recent decade, Building Information Modelling (BIM) has widely been adopted in the Architecture, Engineering and Construction (AEC) industry and completely upended the way we build. While BIM continues gain momentum in the industry, it has also attracted increasing attentions from researchers. However, most of the current study focuses on reviewing BIM for management, BIM for green building, BIM for infrastructure and BIM for Facilities Management (FM). There are few studies about Global BIM review and to discuss their complex inter-connections. In this study, we adopted a scientometric analysis method to review global BIM research from 2004-2019. A total of 1455 scholarly bibliographic records obtained from Web of Science Core Collection databased were established for the analysis. This study has identified the top productive and influential researchers, research institutes, regions/countries, subject categories and journals in the BIM field. In addition, 11 clusters of Global BIM research were also identified including construction project, green BIM, construction safety planning, automated IFC-based workflow and so on. Authors distinguished 11 clusters of global BIM research into 3 stages, namely formulating stage, accelerating stage and transforming stage. Furthermore, authors reviewed the BIM policy of Singapore and observed there is a co-production relationship between evolution of BIM policy and global BIM research. These findings provide valuable information for researchers, practitioners and policy makers by visualizing the current progress in the research field of BIM and highlighting future research needs.

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

String matching is an important part in many real world applications. It must robust against variations in string field. In record linkage for two different datasets matching should detect two patients in common in spite of small variations. But it becomes difficult in case of confidential data because sometimes data sharing between organizations become restricted for privacy purposes. Several techniques have been proposed on privacy-preserving approximate string matching such as Secure Hash Encoding etc. Relative to other techniques for approximate string matching Homomorphic encryption is very new. In this paper we have proposed a Homomorphic Encryption based approximate string matching technique for matching multiple attributes. There is no solution currently available for multiple attributes matching using Homomorphic encryption. We have proposed two different methods for multiple attributes matching. Compare to other existing approaches our proposed method offers security guarantees and greater matching accuracy.

The application of evolutionary optimization algorithms in problem solving is currently gaining wide popularity. Use of Differential Evolution (DE) algorithm in obtaining analytically approximate solution of unstable second order initial value Ordinary Differential Equation (ODE) is presented in this work. The methodology involves solving an associated problem of optimization with con-strains to get an analytically approximate solution for the ODE under consider-ation. Three test cases were used to demonstrate the efficiency of our method. In comparison with other methods discussed in the literature, our method gave significant improvement on the accuracy of the obtained results.

In this paper a new approximate procedure is developed for calculating the inclination angle of the end points of statically determinate beams. The method is based on the topology comparison of simple (hinge-roller combination) supported beam and a resemblant cantilever beam. Assuming that the support reactions of the beam are active forces, the virtual displacements at the points of the reaction forces are calculated. Based on these values the inclination angle is calculated. Several examples are considered and the suggested in this paper, while the procedure is applied for various types of structures and loadings. The results, obtained by the suggested numerical procedure, are compared with analytical ones, and they are in good agreement.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

Mutations in KRT1 (keratin 1) or KRT10 (keratin 10) underlie a spectrum of diseases known as keratinopathic ichthyoses. Epidermolytic ichthyosis (EI) is caused by heterozygous missense mutations in the genes KRT1 or KRT10, mutations in the gene KRT2 (keratin 2) lead to superficial epidermolytic ichthyosis, and congenital reticular ichthyosiform erythroderma is caused by frameshift mutations in the genes KRT10 or KRT1, which lead to the phenomenon of revertant mosaicism. Epidermolytic ichthyosis is also present in a mosaic pattern known as epidermolytic (acantholytic) nevus, isolated or diffuse. In the latter case, gonadic involvement is possible, leading to a rare pedigree in which a parent with diffuse epidermolytic nevus (linear EI) gives birth to a child affected by EI. We present here an update on the phenotypic presentations of keratinopathic ichthyoses and their molecular mechanisms.

Combining modern thermodynamics theory branches, including finite time thermodynamics or entropy generation minimization, constructal theory and entransy theory, with metallurgical process engineering, this paper provides a new exploration on generalized thermodynamic optimization theory for iron and steel production processes. The theoretical core is to thermodynamically optimize performances of elemental packages, working procedure modules, functional subsystems, and whole process of iron and steel production processes with real finite-resource and/or finite-size constraints with various irreversibilities toward saving energy, decreasing consumption, reducing emission and increasing yield, and to achieve the comprehensive coordination among the material flow, energy flow and environment of the hierarchical process systems. A series of application cases of the theory are reviewed. It can provide a new angle of view for the iron and steel production processes from thermodynamics, and can also provide some guidelines for other process industries.

In this paper, we investigate the generalized Padovan sequences and we deal with, in detail, four special cases, namely, Padovan, Perrin, Padovan-Perrin and modified Padovan sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

In this paper, we introduce the generalized Tetranacci quaternions and present some properties of these quaternions.

This paper investigates generalized Bayesian (GB) inference in the context of a one-parameter Pareto distribution. The study focuses on the derivation of generalized Bayesian estimators (GBE) and generalized empirical Bayesian estimators (GEBE) for the parameters of the Pareto distribution using type II censored data. In addition, the study investigates a one-sample prediction approach to examine generalized Bayesian prediction (GBP) and generalized empirical Bayesian prediction (GEBP). To evaluate the performance of these estimation and prediction methods, Monte Carlo simulations were performed comparing GBE with GEBE and GBP with GEBP for different parameter values and learning rate parameters (LRP).

Small peptides (SPs), ranging from 5 to 100 amino acids, play integral roles in plants due to their diverse functions. Despite their low abundance and small molecular weight, SPs intricately regulate critical aspects of plant life, including cell division, growth, differentiation, flowering, fruiting, maturation, and stress responses. As vital mediators of intercellular signaling, SPs have garnered significant attention in plant biology research. This comprehensive review delves into SPs' structure, classification, and identification, providing a detailed understanding of their significance. Additionally, we summarize recent findings on the biological functions and signaling pathways of prominent SPs that regulate plant growth and development. The review also offers a forward-looking perspective on future research directions in peptide signaling pathways.

While considering the sensitivity over the parameter optimization, it is essential to determine which parameters have the most significant implications on model performance. This study focuses on the baseflow recession constant as one of the independent basin parameters to forecast low flows, perform hydrograph analysis, and calibrate rainfall-runoff models for significant improvement. Prior studies examined that the optimization of data adjustment parameters can improve the hydrological model performance and determine the minimum acceptable data length for data scarce regions using the Xinanjaing model. However, it is essential to pay special attention to the sensitivity of the recession constant, which can also impact the model performance during the data scarcity. Therefore, this study extends the research to comprehend the recession constant sensitivity over data adjustment parameters in the shorter datasets leading to more reliable parameter estimation. In terms of that, this study explores how recession constant affects hydrological parameter estimation on annual scale while keeping data adjustment parameters constant in continuous hydrological modeling, employing the Xinanjiang (XAJ) model as a case study. This study considered two approaches of recession constant (cg); (i) assessing the relationship between cg and the data adjustment parameter (Cep), for the 28-year datasets, (ii) investigating the significant impacts of the sensitivity of cg over Cep in shorter datasets which can affect the estimation of the acceptable minimum data length in the data scarce basins. The study underscores the importance of the recession constant sensitivity for reliable continuous hydrological model predictions, especially in data-scared areas. The study’s outcomes enhance the understanding of the importance of parameter sensitivity and its relationship in conceptual hydrological modeling during the data limitations.

Background: Previous in vitro and in vivo studies have demonstrated that storage of cooked rice at 4 °C for 24 h and reheating to 65 °C significantly reduced starch digestibility and postprandial glycaemic responses. Moreover, the effect was greater for parboiled rice compared to other rice varieties commonly consumed in New Zealand. This study aimed to evaluate consumer preferences of related sensory attributes and consumer acceptability of several rice varieties freshly cooked or reheated. Method: Sixty-four consumers volunteered and recorded on Visual Analoge Scales their preference and acceptability of freshly prepared or cold-stored and reheated medium grain white, medium grain brown and parboiled rice. Results: All six rice samples were accepted by participants (average 54%). Reheated parboiled rice and reheated medium grain brown rice were both accepted by participants as a preferred staple meal compared to other rice samples. Among all rice samples, the sweetness and the flavour of freshly cooked warm medium-grain white rice were less preferred (scored 42.1% and 45.0% respectively) compared with other samples (P = 0.05). Participants who prepared and consumed brown rice at home regularly (more than 10 times per month), preferred the reheated brown rice (73.8% (67.4, 80.2)) and reheated parboiled rice (74.3% (67.9, 80.7)) (P < 0.001). Conclusions: It is suggested that reheated parboiled rice, with the lowest starch digestibility and glycaemic impact (both in vitro glucose release and in vivo glucose response) could be accepted as a healthier alternative for the daily staple meal.

Liquid-liquid phase separation (LLPS) of proteins has been found ubiquitously in eukaryotic cells, critical in the controlling of many biological processes through forming a temporary condensed phase with different bimolecular components. TDP-43 is recruited to stress granules in cells and is the main component of TDP-43 granules and proteinaceous amyloid inclusions in patients with amyotrophic lateral sclerosis (ALS). TDP-43 low complexity domain (LCD) is able to demix in solution forming the protein condensed droplets. The molecular interactions regulating its LLPS were investigated at the protein fusion equilibrium stage, where the droplets stopped growing. We found the molecules in the droplet were still liquid-like but with enhanced intermolecular helix-helix interaction in the LCD. The protein would start to aggregate after about 200 minutes of lag time and aggregate slower than at the condition when the protein does not phase separate or the molecules have a reduced intermolecular helical interaction. A structural transition intermediate towards protein aggregation was also discovered involving a decrease of the intermolecular helix-helix interaction and a reduction in the helicity. Therefore, LLPS and the intermolecular helical interaction could help maintain the stability of TDP-43 LCD.

This article develops duality principles applicable to originally non-convex primal variational formulations. More specifically, as a first application, we establish a convex dual approximate variational formulation for a non-linear Kirchhoff-Love plate model. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such a convex dual approximate formulation obtained may be applied to a large class of similar models in the calculus of variations. Finally, in the last section, we present a duality principle and respective convex dual formulation for a Ginzburg-Landau type equation.

The security of several fully homomorphic encryption (FHE) schemes depends on the intractability assumption of the approximate common divisor (ACD) problem over integers. Subsequent efforts on solving the ACD problem as well as its variants were also developed during the past decade. In this paper, an improved orthogonal lattice (OL) based algorithm, AIOL, is proposed to solve the general approximate common divisor (GACD) problem. The conditions for ensuring the feasibility of AIOL are also presented. Compared to the Ding-Tao’s OL algorithm, the well-know LLL reduction is used only once in AIOL, and when the error vector r is recovered in AIOL, the possible difference between the restored and the true value of p is given. The experimental comparisons towards the Ding-Tao’s algorithm and ours are also provided for validating our improvements.

This article has two objectives. Firstly, we will use the vector variational-like inequalities problems to achieve local approximate (weakly) efficient solutions of Vector Optimization Problem within the novel field of the Hadamard manifolds. Previously, we will introduce the concepts of generalized approximate geodesic convex functions and illustrate them with examples. We will see the minimum requirements under which critical points, solutions of Stampacchia and Minty weak variational-like inequalities and local approximate weakly efficient solutions can be identified, extending previous results from the literature for linear Euclidean spaces. Secondly, we will show an economical application, using again solutions of the variational problems to identify with Stackelberg equilibrium points on Hadamard manifolds and under geodesic convexity assumptions.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

The accompanying mechanical behavior during the flow of ore-rock dispersion is an important factor leading to the instability and failure of the orepass in the ore storage section. It is of great significance to accurately understand the instability characteristics of the well wall in the ore section, during the ore drawing process by understanding the flow characteristics and internal mechanical transfer mechanism of ore-rock dispersion. Using the discrete element method to analyze the flow characteristics, contact compactness, stress distribution characteristics and contact force probability distribution of the ore-rock dispersion, it realizes the quantitative characterization of the damage degree of ore-rock flow, and reveals the damage mechanism of mine storage wall. The results show that: (1) The friction between ore-rock particles, between ore-rock and well wall is an important reason for the change of the macroscopic flow form of ore-rock from “one” to “V” type. (2) The compactness and stress concentration of ores are increasing with the increase of storage depth, which is shown that with the increase of storage depth, the greater the probability of well wall instability. (3) The probability distribution of contact force strength between particles decreases exponentially in the whole process of ore drawing, in which the strong chain plays a major role in the stability of the dispersion system. (4) The number of overpressure and the overpressure coefficient can be used to quantitatively characterize the wall damage degree under the action of ore-rock flow. The dynamic side pressure decreases periodically in the form of exponential fluctuations, and the dynamic load formed by the ore-rock flow mainly played a role in the lower area of the ore storage section.

This work aims to generate some types of M_(j )–neighborhoods. Relationships among these M_(j )-neighborhoods and some other types of neighborhoods are discussed. Additionally, M_(j )-lower, M_(j )-upper approximations and M_(j )-accuracy in terms of M_(j )-neighborhoods are presented. Their properties, with some examples, are investigated. Finally, We addressed the comparisons among M_(j )approach and other approaches.

On the basis of the force and safety factor analysis of traditional retaining wall, a new analytical method of force and displacement of slope is suggested, the numerical theoretical solution of the stress distribution of the sliding body can be obtained under the conditions, which the stresses distribution are satisfied with the differential equilibrium equations, the boundary conditions, the compatibility equation and the macroscopic equilibrium equations. The interface stresses between the sliding body and the retaining wall are continuous, the theoretical solution of retaining wall stress distributions can be gotten, while the stress differential equilibrium equation, the compatibility equation, macroscopic force and moment balance equations are satisfied. The strain and displacement solutions can be obtained by using Duncan Chang and Hooke constitutive equations for the slope and the retaining wall respectively. The transfer station of landfill in the Guandukou Town of Badong County is taken as an example, the results of the sliding body and retaining wall analysis show: The stress and strain solutions of a slope and a retaining wall can be obtained by the proposed method, the forces between the retaining wall and the sliding body include shear stress and normal stress, and the stress distributions change with the deformation of the sliding body, the shape and material of retaining wall can be optimized according to the calculation results，it is feasible for the proposed analysis method of slope with retaining wall design to be run many years.

The broad emission bump in the electromagnetic spectra observed following the detection of gravitational waves created during the kilonova event of merger of two neutron stars in August 2017, GW170817, has been linked to the heavy elements of lanthanides (Z=57-71), and a new understanding of creation of heavy elements in the r-process. The initial spectral emission bump has a wavelength range of 3000 - 7000 \AA, thus covering the region of ultraviolet (UV) to optical (O) wavelengths, and is similar to those seen for lanthanides. Most lanthanides have large number of closely lying energy levels which introduce extensive sets of radiative transitions which often form broad region of lines of significant strength. The current study explores these broad features through photoabsorption spectroscopy of 25 lanthanides ions, Ho I-III, Er I-IV, Tm I-V, Yb I-VI and Lu I-VII. With excitations only to a few orbitals up beyond the ground configurations, we find most of these ions cover large number of bound levels with open $4f$ orbital and produce tens to about hundred thousands lines that may form one or multiple broad features in X-ray to UV, O, and infrared (IR) regions. Spectrum of each of 25 ions is presented indicating presence, shape and wavelength region of the features. Accuracy of atomic data to interpret the merger spectra has been a outstanding problem. The present study aims at providing improved atomic data for energies and transition parameters obtained using relativistic Breit-Pauli approximation implemented in the atomic structure code SUPERSTRUCTURE. The present data have been benchmarked with available experimental data for energies and transition parameters. The study finds that number of ions under the present study are possible contributors of the emission bump of GW170817. All atomic data will be made available online at NORAD-Atomic-Data database.

The classical limit definition of a derivative is expressed in a more general form. The general form includes two arbitrary functions of the parameter for which the limit is calculated. A special case of the general form, which includes scaling and translational symmetry transformations of the limiting parameter, is also discussed. The errors in using the classical definition and the generalized form are calculated for small values of the limiting parameter. The derivatives of some known functions are proven using the new definition. For some well-known functions, a suitable selection of the generalized form may introduce simplicity in calculating the derivatives.

In this paper, it is introduced the notion of r-fuzzy β-T_i, i = 0, 1, 2 separation axioms related to a fuzzy operator β on the initial set X which is a generalization of previous fuzzy separation axioms. An r-fuzzy α-connectedness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of r-fuzzy connectedness. An r-fuzzy α-compactness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of fuzzy compactness.

We study the Gaudin models with gl(1|1) symmetry that are twisted by a diagonal matrix and defined on tensor products of polynomial evaluation gl(1|1)[t]-modules, extending all the results of to the twisted case. Namely, we give an explicit description of the algebra of Hamiltonians (Gaudin Hamiltonians) acting on tensor products of polynomial evaluation gl(1|1)[t]-modules and show that there exists a bijection between common eigenvectors (up to proportionality) of the algebra of Hamiltonians and monic divisors of an explicit polynomial written in terms of the highest weights and evaluation parameters. In particular, our result implies that each common eigenspace of the algebra of Hamiltonians has dimension one. We also give dimensions of the generalized eigenspaces.

Background: Globally, hot cooked refined rice is consumed in large quantities and is a major contributor to dietary glycaemic load. This study aimed to compare the glycaemic potency of hot and cold stored parboiled rice to widely available medium grain white rice. Method: Twenty-eight healthy volunteers participated in a three treatment experiment where postprandial blood glucose was measured over 120 minutes after consumption of 140g of rice. Three rice samples were freshly cooked medium-grain white rice, freshly cooked parboiled rice, and parboiled rice stored overnight at 4 ºC. All rice was served warm at 65 ºC. Chewing time was recorded. Results: The 24-hours cold-stored and reheated parboiled rice resulted in a 42% and 12% lower blood glucose concentration trajectory than freshly cooked medium-grain white rice and freshly cooked parboiled rice. Chewing time for 10g cold stored parboiled rice was 6 seconds (25%) longer and was considered more palatable, visually appealing and better tasting than freshly cooked medium grain (all P<0.05). Conclusions:. For regular consumers of rice reheating cooked rice after cold storage would lower the dietary glycaemic load and long term may reduce risk for type 2 and gestational diabetes. More trials are needed to identify the significance.

As a vital component of the terrestrial ecosystem, grassland accounts for one-third of the global vegetation system. Grassland degradation has been exacerbated due to extreme overgrazing in China's Inner Mongolia Autonomous Region (IMAR). While conservation was carried out as the Ecological Subsidy and Award Program (ESAP) to mitigate grassland degradation, little is known about its effectiveness in improving the biophysical conditions of grassland. This paper integrates the conceptual frameworks of total socio-environmental systems to assess how ecological systems respond to ESAP, investigate spatial heterogeneity of ESAP, and explore the meddling effects of socio-environmental interactions on ESAP. We integrate ecological, climate, and socioeconomic data and developed several hierarchical linear mixed models (HLMM) to investigate how these factors interact with ESAP in IMAR. Our findings prove that the above-ground biomass between 2011 and 2015 responds significantly to variations in socioeconomic conditions and ecological communities. Available land resources, hospital and medical facilities, and net farmer and herdsman income are the most critical factors contributing to grassland productivity. Primary industries like mining, total consumer retail value, farming, forestry, animal husbandry, fishery productions, and GDP are the most damaging factors affecting biomass. Our study recommends a regionally or locally tailored ecological recovery policy, instead of a generalized one, in the future effort to conserve grassland.

Abstract: Bacillus subtilis fmb60, which has broad-spectrum antimicrobial activities was isolated from plant straw compost. A hybrid NRPS/PKS cluster was screened from the genome. Sixteen secondary metabolites produced by the gene cluster were isolated and identified using LC-HRMS and NMR. Three lipoamides D–F (1-3) and two amicoumacin derivatives, amicoumacins D, E (4, 5), were identified, and are reported here for the first time. Lipoamides D–F exhibited strong antibacterial activities against harmful foodborne bacteria, with the MIC ranging from 6.25 to 25 µg/mL. Amicoumacin E scavenged 38.8% of ABTS+ radicals at 1 mg/mL. Direct cloning and heterologous expression of the NRPS/PKS and ace gene cluster identified its importance for the biosynthesis of amicoumacins. This study demonstrated that there is a high potential for biocontrol utilization of B. subtilis fmb60, and genome mining for clusters of secondary metabolites of B. subtilis fmb60 has revealed a greater biosynthetic potential for the production of novel natural products than previously anticipated.

For Convolutional Neural Network (CNN), Depthwise Separable CNN (DSCNN) is a preferred architecture for Application Specific Integrated Circuit (ASIC) implementation on edge devices. It can benefit from a multi-mode approximate multiplier proposed in this work. The proposed approximate multiplier uses two 4-bit multiplication operations to implement a 12-bit multiplication operation by reusing the same multiplier array. With this approximate multiplier, sequential multiplication operations are pipelined in a modified DSCNN to fully utilize the PE array in the convolutional layer. This Approximate (A-DSCNN) was implemented on TSMC 40-nm CMOS process with a supply voltage of 0.9 V. At the clock frequency of 200 MHz, the design achieves 4.78 GOPs/mW while occupying 1.24 mm x 1.24 mm silicon area. Compared to conventional DSCNN implemented in a similar process node, the chip area and power consumption were reduced by 53% and 25%, while the throughput was improved by 17%.

Based on some geometrical properties of the Rabinovich system the closed-form solutions of the equations has been established. Moreover the Rabinovich system is reduced to a nonlinear differential equation depending on an auxiliary unknown function. The approximate analytical solutions are built using the Optimal Auxiliary Functions Method (OAFM). A good agreement between the analytical and corresponding numerical results has been performed. The accuracy of the obtained results emphasizes that this procedure could be successfully applied for more dynamical systems with these geometrical properties.

Imitation learning, also known as programming by demonstration, has been shown to be a promising paradigm for intuitive robot programming by non-expert users. However, the classical kinesthetic approach with physical hand guidance suffers from generalizability across different robot types and is impractical for demonstrating tasks with long horizons. Visual imitation learning enables the recording of multi-step tasks as a single continuous video, allowing non-experts to demonstrate tasks naturally. Existing approaches typically require a large amount of data to develop end-to-end deep learning models that map raw pixels to robot actions. This paper explores the application of visual imitation learning from one-shot demonstration, significantly reducing the data requirements and simplifying the programming process. To achieve this target, a framework is proposed to map hand trajectories to the robot end-effector, consisting of four essential components: hand detection; object detection; segmentation of the trajectories into elemental skills; and learning the skills. Methods are developed for each component and evaluated on recorded videos to demonstrate the effectiveness of the proposed framework.

This research focuses on the Hopf bifurcation occurring at a singular point with high-order degeneracy in a class of three-dimensional systems. Based on center manifold theorem, by expanding the technique for determining singular point values of degenerate singularities in two-dimensional systems, the formal series method to determine the singular point values at the high-order degenerate critical point is discussed. Furthermore, a class of specific three-dimensional differential systems with high-order degenerate singularities is explored. By computing the singular point values and determining center conditions, we proved that a minimum of 5 small-amplitude limit cycles in the vicinity of the origin. This research provides new perspectives on the center problem and limit cycle bifurcation in high-dimensional systems with high-order degenerate singular points.

Interpore hydrates are the main occurrence forms of marine gas hydrates. Pore characteristics are a vital factor affecting the thermodynamic properties of hydrates and their distribution in sediments. Currently, the characterization of the pore system for hydrate-bearing reservoirs are little reported. Therefore this paper focus on the Krishna-Godavari Basin, via varies methods to characterize the hydrate-bearing sediments in the region. The results showed that X-ray Diffraction(XRD) combined with Scanning Electron Microscope (SEM)and Cast Thin Section (CTS) can better characterize the mineral composition in the reservoir, High Pressure Mercury Injection (HPMI) focused on the contribution of pore size to permeability, Constant Rate Mercury Injection(CRMI) had the advantage of distinguishing between pore space and pore throat, and Nuclear Magnetic Resonance Cryoporometry (NMRC) technique can not only obtain the pore size distribution of nanopores with a characterization range greater than Nitrogen Gas Adsorption (N2GA), but also quantitatively describe the trend of fluids in the pore system with temperature. As for pore system, Samples 58 and 68 all developed nanopores, the mineral distribution was relatively scattered, and they were rich in paleontological shells such as foraminifera, among which Sample 68 had more pyrite content, and abundant pyrite framboid was observed, which made the intergranular pore develop and provide more nanopores. Sample 58 has a high concentration of pore and throat, high pore connectivity, low pore curvature, and pores with a diameter of 10μm contributing to the main permeability, with an average pore radius of 2.495μm, whereas Sample 68 has poor pore connectivity, high curvature, and pores with a diameter of 1μm contributing to the main permeability, with an average pore diameter of 60 nm, which explains the obvious difference in permeability between the two samples.

High dimensional statistical analysis for the yield of large-scale circuits is quite difficult due to expensive simulations, especially for the memory circuits with high sigma requirement (e.g., SRAM). In this paper, we developed an efficient sparse additive model to substitute simulations. To fit high sigma region accurately, the modeling center is moved to near failure boundary searched by scaling the shape of sampling function. To solve the model efficiently, the process variables are grouped by standard cells so that the model can be solved by our developed blockwise greedy algorithm. The experiments on the 28nm memory circuits validate that our method achieves high accuracy and efficiency compared with other state-of-art works.

Over the past decades, overweight and obesity has become a global epidemic and the leading threat for death. To prevent the serious risk, an overweight or obese individual must apply a long-term weight-management strategy to control food intake and physical activities, which is however, not easy. Recently, with the advances of information technology, more and more people can use wearable devices and smartphones to obtain physical activity information, while they can also access various health-related information from Internet online social networks (OSNs). Nevertheless, there is a lack of an integrated approach that can combine these two methods in an efficient way. In this paper, we address this issue and propose a novel mobile-social framework for health recognition and recommendation, namely, H-Rec². The main ideas of H-Rec² include (1) to recognize the individual's health status using smartphone as a general platform, and (2) to recommend physical activity and food intake based on personal health information, life science principles, and health-related information obtained from OSNs. To demonstrate the potentials of the H-Rec² framework, we develop a prototype that consists of four important components: (1) an activity recognition module that senses physical activity using accelerometer, (2) a health status modeling module that applies a novel algorithm to generate personalized health status index, (3) a restaurant information collection module that collects relevant information from OSN, and (4) a restaurant recommendation module that provides personalized and context-aware recommendation. To evaluate the prototype, we conduct both objective and subjective experiments, which confirm the performance and effectiveness of the proposed system.

Generalized Bayesian (GB) is a Bayesian approach based on the learning rate parameter (LRP) () as a fraction of the power of the likelihood function. In this paper, we consider the GB method to perform inference studies for a class of exponential distributions. Generalized Bayesian estimators (GBE) and generalized empirical Bayesian estimators (GEBE) for the parameters of the considered distributions were obtained based on the censored type II samples. In addition, generalized Bayesian prediction (GBP) and generalized empirical Bayesian prediction (GEBP) were considered using a one-sample prediction scheme. Monte Carlo simulations were performed to compare the performance of the GBE and GEBE estimation results and the GBP and GEBP prediction results for different values of the LRP.

Let an odd integer \(\mathcal{X}\) be expressed as $\left\{\sum\limits_{M > m} b_M 2^M\right\} + 2^m - 1,$ where $b_M \in \{0, 1\}$ and $2^m - 1$ is referred to as the Governor. In Collatz-type functions, a high index Governor is eventually reduced to $2^1 - 1$. For the $3\mathcal{Z} + 1$ sequence, the Governor occurring in the Trivial cycle is $2^1 - 1$, while for the $5\mathcal{Z} + 1$ sequence, the Trivial Governors are $2^2 - 1$ and $2^1 - 1$. Therefore, in these specific sequences, the Collatz function reduces the Governor $2^m - 1$ to the Trivial Governor $2^{\mathcal{T}} - 1$. Once this Trivial Governor is reached, it can evolve to a higher index Governor through interactions with other terms. This feature allows $\mathcal{X}$ to reappear in a Collatz-type sequence, since $2^m - 1 = 2^{m - 1} + \cdots + 2^{\mathcal{T} + 1} + 2^{\mathcal{T}} + (2^{\mathcal{T}} - 1).$ Thus, if $\mathcal{X}$ reappears, at least one odd ancestor of $\left\{\sum\limits_{M > m} b_M 2^M\right\} + 2^{m - 1} + \cdots + 2^{\mathcal{T} + 1} + 2^{\mathcal{T}} + (2^{\mathcal{T}} - 1)$ must have the Governor $2^m - 1$. Ancestor mapping shows that all odd ancestors of $\mathcal{X}$ have the Trivial Governor for the respective Collatz sequence. This implies that odd integers that repeat in the $3\mathcal{Z} + 1$ sequence have the Governor $2^1 - 1$, while those forming a repeating cycle in the $5\mathcal{Z} + 1$ sequence have either $2^2 - 1$ or $2^1 - 1$ as the Governor. Successor mapping for the $3\mathcal{Z} + 1$ sequence further indicates that there are no auxiliary cycles, as the Trivial Governor is always transformed into a different index Governor. Similarly, successor mapping for the $5\mathcal{Z} + 1$ sequence reveals that the smallest odd integers forming an auxiliary cycle are smaller than $2^5$. Finally, attempts to identify integers that diverge for the $3\mathcal{Z} + 1$ sequence suggest that no such integers exist.

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum spacetime. It is based in the Minimum Group Representation Principle (MGRP). Within this framework new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space-times. Our main results here are: {\bf(i)} We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, as the spectral scalar and tensor indices, $n_S$ an $n_T$, and the tensor to scalar ratio $r$. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. {\bf(ii)} The pure entangled states in the minimum group (metaplectic) $Mp(n)$ representation for quantum de Sitter space-time and black holes are found. {\bf(iii)} For entanglement, the relation between the Schmidt type representation and the physical states of the $Mp(n)$ group is found: This is a {\it new non-diagonal} coherent state representation complementary to the known Sudarshan diagonal one. {\bf(iv)} Mean value generators of $Mp(2)$ are related to the adiabatic invariant and topological charge of the spacetime (matrix element of the transition $-\infty < t < \infty$). {\bf(v)} The basic {\it even} and {\it odd} $n$-sectors of the Hilbert space are intrinsic to the quantum spacetime and its discrete levels (in particular continuum for $n \rightarrow \infty$), they do not require any extrinsic generation process as the standard Schrodinger cat states, and are {\it entangled}. {\bf(vi)} The gravity or cosmological domains in one side and another of the Planck scale are {\it entangled}. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity reqion and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space-time are entangled. {\bf(vii)} The general classical-quantum gravity duality is associated to the Metaplectic $Mp(n)$ group symmetry which provides the complete full covering of the phase space and of the quantum space-time mapped from it.

Background: Periodontitis is a disease that leads to serious functional and aesthetic dysfunctions resulting in impairment of life quality; it exists in different forms and its etiology is related with multiple component causes. Angiogenesis, together with inflammatory infiltrate, are two key processes in the evolution of inflammatory processes involving gingival tissues. The aim of this study was to evaluate their alterations in relation to some important periodontal diseases-associated factors (i.e. smoke, sex, age, plaque, pus, probing pocket depth) in patients with diagnosis of Generalized Aggressive Periodontitis (GAP). Methods: Eighteen subjects with GAP were enrolled for this study. Percentage of inflammatory cells and vascular area were measured and evaluated in relation with each periodontal diseases-associated factor. Results: The results showed a significant decrease of the percentage of vascular area in association with almost all the periodontal diseases-related factors (smoke, age, PPD, plaque) and not significant differences in the percentage of inflammatory cells. Conclusions: Data suggest that, even if these factors are often commonly related to worsening of periodontal status, they did not affect inflammatory and vascular pattern, as we can assume. For the future, additional studies, aimed to evaluated each singular factor in a wider sample size, should be planned.

Innovative interventions in the planning and design of stair and escalator facilities call for understanding their effects on stair use. This study considers five planning variables for the twinned stair and escalator facilities–stair pitch and width, angle of deviation, height and separating distance. Public sites were identified in 8 commercial districts in Beijing. Facilities (n=21) presenting heterogeneously across variables were sampled for simultaneous up and down pedestrian counts in 18 5-minute video segments middays, for a total of 1464 counts. Stair width accounts for 20% of the variance in ascending rate and 10% in descending. Plan angle accounts for 2% in ascending and 5% in descending, while pitch accounts for 1% in ascending and 5% in descending. The study confirms the effects of layout and design of stairway and escalator facilities on facility choice. The results point directly to interventions in support of higher stair-climbing rates.

Predators are dependent on the capture of prey to meet their energetic and nutritive requirements, imposing a regime of predation risk. Consequently, prey experience both consumptive and non-consumptive effects. Non-consumptive effects may manifest through altered growth and ontogenetic trajectories of prey species, a dynamic modulated by olfactory or other sensory cues from predators. Bactrocera dorsalis Hendel represents a great invasive threat to global horticulture. While earlier research has primarily centered on the consumptive interactions between B. dorsalis and its natural enemies, the potential consequences of non-consumptive interactions on the development of B. dorsalis have been overlooked. In this study, we investigated the impact of predation risk effects, induced by both visual exposure to the predatory mantis Hierodula patellifera Serville and its associated odor, on the life history traits of B. dorsalis. Female B. dorsalis demonstrated reduced development time in the presence of isolated H. patellifera or H. patellifera odor, yet evidenced significantly increased fecundity. Conversely, males displayed no significant change in development time. Additionally, neither female nor male body weight at death was significantly influenced by predation risk from isolated predators or predator odor. These results indicated adaptive developmental strategies of B. dorsalis when faced with risks from predators and highlight the important role of predator odor, which has the potential to lay the groundwork for improving biological control efforts and innovative approaches within pest control.

Epitaxial lithium ferrite (LiFe5O8) films with different thicknesses have been successfully fabricated on SrTiO3 (001) substrates by magnetron sputtering deposition technique. The microstructural and magnetic properties are characterized by advanced transmission electron microscope and magnetic measurement device. It was found that the formation of structural defects can be influenced by the thickness of the film. Apart from the misfit dislocations, the orientation domains form in thinner film and twin boundaries appear in thicker film, respectively, contributing to the misfit strain relaxation in the heterosystem. The magnetic measurement shows that the thinner films have enhanced magnetization and a relatively lower coercive field compared with the thicker films containing the antiferromagnetic twin boundaries. Our results provide a way for tuning the microstructure and magnetic properties of lithium ferrite films by changing the film thickness.

We introduce a new generalized inverse (i.e., generalized EP element) which is a natural generalization of EP and *-DMP elements in a Banach *-algebra. We present polar-like characterizations of generalized EP elements. The necessary and sufficient conditions under which the sum of two generalized EP elements is a generalized EP element are investigated. Finally, the generalized core-EP orders for generalized EP elements are characterized.

One open question remains regarding the theory of the generalized variational principle, that is, why the stress-strain relation still be derived from the generalized variational principle while the Lagrangian multiplier method is applied in vain? This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics. As long as the functional has one of the combination $A(\epsilon_{ij})-\sigma_{ij}\epsilon_{ij}$ or $B(\sigma_{ij})-\sigma_{ij}\epsilon_{ij}$, its corresponding variational principle will produce the stress-strain relation without the need to introduce extra constraints by the Lagrangian multiplier method. It is proved herein that the Hu-Washizu functional $\Pi_{HW}[u_i,\epsilon_{ij},\sigma_{ij}]$ and Hu-Washizu variational principle comprise a real three-field functional.

In this paper, we introduce the generalized dual hyperbolic Fibonacci numbers. As special cases, we deal with dual hyperbolic Fibonacci and dual hyperbolic Lucas numbers. We present Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan's, Cassini's, d'Ocagne's, Gelin-Cesàro's, Melham's identities and present matrices related with these sequences.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

This work emphasizes some geometrical properties of the Maxwell--Bloch equations. Based on these properties the closed-form solutions of their equations are established. Thus, the Maxwell-Bloch equations are reduced to a nonlinear differential equation depending on an auxiliary unknown function. The approximate analytical solutions were built using the Optimal Homotopy Asymptotic Method (OHAM). A good agreement between the analytical and corresponding numerical results was found. The accuracy of the obtained results is validated through the representative figures. This procedure could be successfully applied for more dynamical systems with geometrical properties.

The famous singlet correlations of a composite quantum system consisting of two spatially separated components exhibit notable features of two kinds. The first kind consists of striking certainty relations: perfect correlation and perfect anti-correlation in certain settings. The second kind consists of a number of symmetries, in particular, invariance under rotation, as well as invariance under exchange of components, parity, or chirality. In this note, I investigate the class of correlation functions that can be generated by classical composite physical systems when we restrict attention to systems which reproduce the certainty relations exactly, and for which the rotational invariance of the correlation function is the manifestation of rotational invariance of the underlying classical physics. I call such correlation functions classical EPR-B correlations. It turns out that the other three (binary) symmetries can then be obtained "for free": they are exhibited by the correlation function, and can be imposed on the underlying physics by adding an underlying randomisation level. We end up with a simple probabilistic description of all possible classical EPR-B correlations in terms of a "spinning coloured disk" model, and a research programme: describe these functions in a concise analytic way.

In order to investigate the relationship between government policy, the service and design of rural crowdsourcing spaces, the self-efficacy of returning youth, and the innovation performance of businesses, this study focuses on gathering data by distributing questionnaires to returning youth in rural crowdsourcing spaces and developing a structural model. The results demonstrate how important government policies are in encouraging youth entrepreneurship in their local communities. It has the potential to enhance both the development of rural crowdsourcing spaces and the self-efficacy of young entrepreneurs, thereby enhancing the innovative capabilities of local entrepreneurial businesses. Therefore, in order to encourage economic development in rural areas, the government should improve pertinent support measures.

Hydrogen is considered as an ideal substitute to the traditional fossil fuels because of its widespread sources, high calorific value of combustion, and zero carbon emissions. The electrocatalytic water-splitting to produce hydrogen is also deemed to be the best approach, however, it is a challenge to make high-efficient and low-cost electrocatalysts. Single-atom catalysts (SACs) are considered the most promising candidate to replace the traditional noble-metal catalysts. Compared with SACs, the dual-atom catalysts (DACs) are of greater attraction including higher metal loading, more versatile active sites, and excellent catalytic activity. In the review, several general synthetic strategies and structural characterization methods of DACs are introduced, and the mechanisms of hydrogen evolution reaction (HER) and oxygen evolution reactions (OER) are discussed. The authors hope that the review has given some insights and inspiration to the researchers about DACs in electrocatalytic water-splitting.

Demethyleneberberine is an active component extracted from the Chinese herbal drug Cortex Phellodendri. It is also a metabolite of the berberine in animals and humans. However, the pharmacokinetics, tissue distribution and excretion of demethyleneberberine have not been reported. The present study aimed to investigate the pharmacokinetic parameters of demethyleneberberine by developing a method of high-performance liquid chromatography-tandem mass spectrometry (LC-MS/MS). The detection was performed by using positive ion electrospray ionization in multiple reaction monitoring mode. The MS/MS ion transitions were monitored at m/z 324.4→308.3 for demethyleneberberine and 465.5→350.3 for IS. After oral administration of demethyleneberberine in rats and mice, the pharmacokinetics, tissue distribution, and excretion of desmethylberberine in rats and mice were comparatively studied for the first time. The plasma concentration of desmethylberberine reached its peak within 5 min after oral administration in both rats and mice. The bioavailability of rats and mice was comparable, ranging from 4.47% to 5.94%, higher than that of berberine. The total excretion of desmethylberberine in urine, feces and bile is 7.28~9.77%. These findings provide valuable insights into the pharmacological and clinical research on desmethylberberine.

Traffic anomaly detection is crucial for urban management, yet current research is often confined to small-scale endeavors. This study collected nine months of real-time Wuhan traffic monitoring data from Amap. We proposed Traffic-ConvLSTM, a multi-scale spatial-temporal technique based on long and short-term memory networks (LSTM) and convolutional neural networks (CNN) to effectively achieve long-term anomaly detection at the city level. First, we convert the traffic flow data into image representation, which enables the capture of the spatial correlation between traffic flow and roads and the correlation between traffic flow and roads, as well as the surrounding environment. Second, The model utilizes convolution kernels of different sizes to extract spatial features at road-level, regional-level, and city-level scales, while incorporating temporal features of different time steps to capture hourly, daily, and weekly dynamics. Additionally, varying weights are assigned to the convolution kernels and temporal features of varying spatio-temporal scales to capture the heterogeneous strengths of spatio-temporal correlations within patterns of traffic anomalies. The proposed Traffic-ConvLSTM model exhibits improved performance over existing techniques in the task of identifying long-term and large-scale traffic anomaly occurrences. Furthermore, the analysis reveals significant traffic anomalies during holidays and urban sporting events. The diverse travel patterns observed in response to various activities offer insights for large-scale urban traffic anomaly management, providing recommendations for city-level traffic control strategies.

Behavior analysis is a widely used non-invasive tool in the practical production routine, as the animal acts as a biosensor capable of reflecting its degree of adaptation and discomfort to some environmental challenge. Predominantly, conventional statistics use occurrence data for behavioral evaluation and well-being estimation, disregarding the temporal sequence of events. The Generalized Sequential Pattern (GSP) algorithm is a data mining method that identifies recurrent sequences that exceed a user-specified support threshold, whose potential has not yet been investigated for broiler chickens in enriched environments. Enrichment aims to increase environmental complexity with promising effects on animal welfare, stimulating priority behaviors and potentially reducing the deleterious effects of heat stress. The objective was to validate the application of the GSP algorithm to identify temporal correlations between heat stress and the behavior of broiler chickens in enriched environments through proof of concept. Video image collection was carried out automatically for 48 continuous hours, analyzing a continuous period of seven hours, from 12:00 PM to 6:00 PM, during two consecutive days of tests for chickens housed in enriched and non-enriched environments under comfort and stress temperatures. Chickens at comfort temperature showed high motivation to perform the behaviors of Preening (P), Foraging (F), Lying down (Ld), Eating (E), and Walking (W) whose sequences &lt;{Ld,P}&gt;; &lt;{Ld,F}&gt;; &lt;{P,F,P}&gt;; &lt;{Ld,P,F}&gt; and &lt;{E,W,F}&gt; were the only ones observed in both treatments. All other sequential patterns (comfort and stress) were distinct, suggesting that environmental enrichment alters the behavioral pattern of broiler chickens. Heat stress drastically reduced the sequential patterns found at the 20% threshold level in the tested environments. The behavior of lying laterally "Ll" is a strong indicator of heat stress in broilers and was only frequent in the non-enriched environment, which may suggest that environmental enrichment provides the animal with better opportunities to adapt to stress-inducing challenges, such as heat.

Genomic sequencing of Alternaria oxytropis OW 7.8 isolated from Oxytropis glabra was performed, the swnK gene was cloned and knocked out firstly. The colony morphology of ΔswnK-ACP differed from that of A. oxytropis OW 7.8, appearing milky white or pale yellow, with irregular shapes and a slower growth rate. SW was not detected in ΔswnK-ACP, indicating that the swnK gene promotes SW synthesis in A. oxytropis OW 7.8. 8 differentially expressed genes (DEGs) and 7 differentially expressed metabolites (DEMs) closely associated with SW biosynthesis were identified in the transcriptome and metabolome analysis of A. oxytropis OW 7.8 and ΔswnK-ACP. The SW biosynthesis pathway in A. oxytropis OW 7.8 was predicted and refined. These results may lay foundation of in-depth analysis of the molecular mechanisms and metabolic pathway of SW synthesis in fungi, and provide reference for future control of SW in locoweed, which would benefit the development of grassland animal husbandry and the sustainable use of grassland ecosystem.

In this study, we first discover some new concept coordinated UD-convex mappings with fuzzy-number values. After that, we look into Hermite-Hadamard type inequalities via fuzzy-number-valued coordinated UD-convex fuzzy-number-valued mapping (coordinated UD-convex FNVM). In the case of coordinated UD-convex FNVM, novel conclusions are derived by making particular decisions in recently proven inequalities. Additionally, it is demonstrated that the recently discovered inequalities are expansions of comparable findings in the literature. It is important to note that the main outcomes are validated by nontrivial examples.