In this paper, we provide alternative proofs to some results proposed in the article "New inequalities involving circular, inverse circular, hyperbolic, inverse hyperbolic and exponential functions" authored by Yogesh J. Bagul.

In this study, we actually want to explore the time-fractional Phi-four equation via two methods, the exp _a function method and the hyperbolic function method. We transform a fractional order dierential equation into an ordinary differential equation using a wave transformation and the fractional derivative in conformable form. Then, the resulting equation has successfully been explored for new explicit exact solutions. The procured solutions are simply showed the effectiveness and plainness of the projected methods.

The aim of this study was to investigate the physicochemical characterization and biological activities of chitosan (CH) based composite films with the incorporation of chestnut flower essential oil (CFEO). The composite films were prepared by casting method and characterized in terms of structural, morphological and mechanical properties via FT-IR, XRD, UV, SEM and TGA. The results proved the significantly increased water vapor permeability (WVP), heat resistance, antibacterial and antioxidant capabilities of CH-CFEO films. The incorporation of CH and CFEO enhanced the UV blocking, which made the film shield almost all UV light. Films with the tensile strength of 6.37 ± 0.41 MPa and elongation at break of 22.57 ± 0.35% were got with 6 mg mL-1 CFEO. Subsequently, the fruit preservation experiments also confirmed that the composite films could effectively extend the shelf life of bananas through their excellent water vapor and oxygen barrier. These desirable performances enable our newly developed composite films to be a remarkable packaging material to solve the fresh fruit preservation dilemma.

This paper presents a new method for parameterizing the Lorentz group based on coupled parameters. From the Euler–Hamilton equations, an additional angular rapidity and perpendicular rapidity are obtained, and the Hamiltonian and Lagrangian of a relativistic particle are expanded into rapidity spectra. A so-called passage to the limit is introduced that makes it possible to decompose physical quantities into spectra in terms of elementary functions when explicit decomposition is difficult. New rapidity-dependent Lorentz-invariant coordinates are obtained, and the descriptions of particle motion using the old and new Lorentz-invariant forms as applied to plane waves are compared. Based on a classical model of particle motion in the field of a plane monochromatic electromagnetic wave and in that of a plane laser pulse, the rapidity-dependent spectral decompositions into elementary functions are presented, and the Euler–Hamilton equations are derived as rapidity functions in 3+1 dimensions.

In this paper we establish several Hermite-Hadamard type integral inequalities for hyperbolic p-convex functions. Applications for special means are provided as well.

This paper proposes a relativistic model of the Universe in which the geometry describes a 4D version of the 2-sheeted hyperboloid that is isotropic, homogeneous in space at a given time and inhomogeneous in time. The radius of this metric is temporal as opposed to spatial. It predicts both a Universe and Anti-Universe moving in opposite directions of time undergoing an expansion phase, followed by a collapsing phase. Using only the current age of the Universe and transition redshift, it predicts the accelerated expansion and it is shown that its Hubble diagram fits currently available supernova and quasar data as well as predicting a Hubble constant H0 ≈ 71.6km/s/M pc. The angular term of the metric describes time dilation caused by the relativistic kinematic precession effect known as Thomas Precession which can be interpreted as spin about the time dimension. The model also makes two novel predictions: that the early Universe should have structures older than expected due to an increased amount of proper time relative to coordinate time in that era and that the background Universe should appear brighter than current models predict

We prove an analog of the removable singularity theorem for bounded harmonic functions on stratified sets. The harmonic functions are understood in the sense of the soft Laplacian. The result can become one of the main technical components for extending the well-known Poincaré–Perron’s method of proving the solvability of the Dirichlet problem for the soft Laplacian.

In this study, based on a new quantum integral identity, the authors establish some quantum estimates of Hermite-Hadamard type inequalities for convex functions. These results generalize and improve some known results given in literatures.

Ptolemy’s Theorem in Euclidean geometry, named after the Greek astronomer and mathematician Claudius Ptolemy, is well known. We translate Ptolemy’s Theorem from analytic Euclidean geometry into the Poincar´e ball model of analytic hyperbolic geometry, which is based on M¨obius addition. The translation of Ptolemy’s Theorem from Euclidean geometry into hyperbolic geometry is achieved by means of the hyperbolic trigonometry, called gyrotrigonometry, to which the Poincar´e ball model gives rise, and by means of the duality of trigonometry and gyrotrigonometry.

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

Deep neural networks with powerful auto-optimization tools have been widely applied in various research fields, e.g., NLP and computer vision. However, existing neural network architectures typically are constructed using different inductive biases, e.g., preconceptions, expecting to decrease parameter search space during training, reduce computational cost or introduce expert knowledge in the neural network design. As an alternative, Multilayer Perceptron (MLP) provides much better freedom for exploration, has a lower inductive bias than convolutional neural networks (CNNs), and offers good flexibility in learning complex patterns. Even though, such neural architectures are commonly built in a flat Euclidean space, which is not necessarily the optimal space for any data, and is especially not good for modeling hierarchical correlations. Hyperbolic neural networks (HNNs) have gained attention for their ability to capture hierarchical structures present in complex data types like graphs. Recently, there has been an increasing interest to extend HNNs to computer vision tasks, motivated by the observations that images possess rich hierarchical relations. However, this is generally applied by employing a Euclidean backbone for learning higher-level semantic representations and only incorporating a hyperbolic classifier for classification, which, we argue, does not make full use of the advantage of hyperbolic space. Considering the recovery of the attention-free Multilayer Perceptron(MLP), in this paper, we extend it to non-Euclidean space and propose a novel architecture, named Hyperbolic Res-MLP (HR-MLP), that leverages fully hyperbolic layers to learn feature embeddings and perform image classification in an end-to-end fashion. With the help of the proposed Lorentz cross-patch and cross-channel layers, we can directly perform operations in the hyperbolic domain with fewer parameters, making it faster to train and providing comparatively better performance than its Euclidean counterpart. Experiments on CIFAR10, CIFAR100, and MiniImageNet demonstrate a comparable and superior performance when compared to Euclidean baselines. Our code is available at (https://github.com/Ahmad-Omar-Ahsan/HR-MLP)

The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic 2ⁿ-dimensional extensions in modeling some genetic and cultural phenomena. Mathematical properties of hyperbolic numbers and their bisymmetric matrix representations are described in a connection with their application to analyze the following structures: alphabets of DNA nucleobases; inherited phyllotaxis phenomena; Punnett squares in Mendelian genetics; the psychophysical Weber-Fechner law; long literary Russian texts (in their special binary representations). New methods of algebraic analysis of the harmony of musical works are proposed, taking into account the innate predisposition of people to music. The hypothesis is put forward that sets of eigenvectors of matrix representations of basis units of 2ⁿ-dimensional hyperbolic numbers play an important role in transmitting biological information. A general hyperbolic rule regarding the oligomer cooperative organization of different genomes is described jointly with its quantum-information model. Besides, the hypothesis about some analog of the Weber-Fechner law for sequences of spikes in single nerve fibers is formulated. The proposed algebraic approach is connected with the theme of the grammar of biology and applications of bisymmetric doubly stochastic matrices. Applications of hyperbolic numbers reveal hidden interrelations between structures of different biological and physical phenomena. They lead to new approaches in mathematical modeling genetic phenomena and innate biological structures.

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.

Elevated carbon dioxide (eCO₂) stimulates wheat grain yield, but simultaneously reduces protein (N) concentration. Also other essential nutrients are subject to change. This study is a comprehensive synthesis of wheat experiments with eCO₂, estimating effects on N, minerals (B, Ca, Cd, Fe, K, Mg, Mn, Na, P, S, Zn), and starch. Analysis was made by i) deriving response functions for the relative effect on element concentration in relation to CO₂ concentration, ii) meta-analysis to test the magnitude and significance of observed effects, and iii) relating CO₂ effects on minerals to effects on N and grain yield. Responses range from zero to strong negative effects of eCO₂ on mineral concentration, with largest reductions for the nutritionally important elements N, Fe, S, Zn and Mg. Together with the positive but small and non-significant effect on starch concentration, the large variation in effects suggests that CO₂-induced responses cannot be explained by a simple dilution model. To explain the observed pattern, uptake and transport mechanisms may have to be considered, along with the link of different elements to N uptake. Our study shows that eCO₂ has a significant effect on wheat grain stoichiometry, with implications for human nutrition in a world of rising CO₂.

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

In this work, Gaussian Tribonacci functions are defined and investigated on the set of real numbers $\mathbb{R},$ \textit{i.e}., functions $f_{G}$ $:$ $\mathbb{R}\rightarrow \mathbb{C}$ such that for all $% x\in \mathbb{R},$ $n\in \mathbb{Z},$ $f_{G}(x+n)=f(x+n)+if(x+n-1)$ where $f$ $:$ $\mathbb{R}\rightarrow \mathbb{R}$ is a Tribonacci function which is given as $f(x+3)=f(x+2)+f(x+1)+f(x)$ for all $x\in \mathbb{R}$. Then the concept of Gaussian Tribonacci functions by using the concept of $f$-even and $f$-odd functions is developed. Also, we present linear sum formulas of Gaussian Tribonacci functions. Moreover, it is showed that if $f_{G}$ is a Gaussian Tribonacci function with Tribonacci function $f$, then $% \lim\limits_{x\rightarrow \infty }\frac{f_{G}(x+1)}{f_{G}(x)}=\alpha \ $and\ $\lim\limits_{x\rightarrow \infty }\frac{f_{G}(x)}{f(x)}=\alpha +i,$ where $% \alpha $ is the positive real root of equation $x^{3}-x^{2}-x-1=0$ for which $\alpha >1$. Finally, matrix formulations of Tribonacci functions and Gaussian Tribonacci functions are given. In the literature, there are several studies on the functions of linear recurrent sequences such as Fibonacci functions and Tribonacci functions. However, there are no study on Gaussian functions of linear recurrent sequences such as Gaussian Tribonacci and Gaussian Tetranacci functions and they are waiting for the investigating. We also present linear sum formulas and matrix formulations of Tribonacci functions which have not been studied in the literature.

Backward electromagnetic waves are extraordinary waves with contra-directed phase velocity and energy flux. Unusual properties of the coherent nonlinear optical coupling of the phase-matched ordinary and backward electromagnetic waves with contra-directed energy fluxes are described which enable greatly-enhanced frequency and propagation direction conversion, parametrical amplification, as well as control of shape of the light pulses. Extraordinary transient processes that emerge in such metamaterials in pulsed regimes are described. The results of the numerical simulation of particular plasmonic metamaterials with hyperbolic dispersion are presented, which prove the possibility to match phases of such coupled guided ordinary and backward electromagnetic waves. Particular properties of the outlined processes in the proposed metamaterial are demonstrated through numerical simulations. Potential applications include ultra-miniature amplifiers, frequency changing reflectors, modulators, pulse shapers, and remotely actuated sensors.

This paper investigates the feasibility of a backend design for real-time, multiple-channel processing digital phased array system, particularly for high-performance embedded computing platforms constructed of using general purpose digital signal processors. Frist, we obtained the lab-scale backend performance benchmark from simulating beamforming, pulse compression, and Doppler filtering based on MicroTCA chassis using Serial RapidIO protocol in backplane communication. Next, a field-scale demonstrator of a multifunctional phased array radar is emulated by using the similar configuration. Interestingly, the performance of a barebone design is compared to that of emerging tools that systematically take advantage of parallelism and multicore capabilities, including Open Computing Language.

In this article, we set up some adequate conditions for analytic functions associated with cosine hyperbolic function. We determine conditions on α such that 1+α (ϰ^(2+P(j-1) ) g^' (ϰ))/(Pg^j (ϰ)),for each j=0,1,2,3 are subordinated by Janowski function, then (g(ϰ))/ϰ^P <cosℏ⁡(ϰ),(ϰ∈C). By choosing specific values of functions g we get some adequate conditions for multivalent starlike function related with cosine hyperbolic.

Scator set, introduced by Fernández-Guasti and Zaldívar, is endowed with a very peculiar non-distributive product. In this paper we consider the scator space of dimension $1+2$ and the so called fundamental embedding which maps the subset of scators with non-zero scalar component into 4-dimensional space endowed with a natural distributive product. The original definition of the scator product is induced in a straightforward way. Moreove, we propose an extension of the scator product on the whole scator space, including scators with vanishing scalar component.

The author's method of oligomer sums for analysis of oligomer compositions of eukaryotic and prokaryotic genomes is described. The use of this method revealed the existence of general rules for cooperative oligomeric organization of a wide list of genomes. These rules are called hyperbolic because they are associated with hyperbolic sequences including the harmonic progression 1, 1/2, 1/3, .., 1/n. These rules are demonstrated by examples of quantitative analysis of many genomes from the human genome to the genomes of archaea and bacteria. The hyperbolic (harmonic) rules, speaking about the existence of algebraic invariants in full genomic sequences, are considered as candidates for the role of universal rules for the cooperative organization of genomes. The described phenomenological results were obtained as consequences of the previously published author's quantum-information model of long DNA sequences. The oligomer sums method was also applied to the analysis of long genes and viruses including the COVID-19 virus; this revealed, in characteristics of many of them, the phenomenon of such rhythmically repeating deviations from model hyperbolic sequences, which are associated with DNA triplets. In addition, an application of the oligomer sums method are shown to the analysis of the following long sequences: 1) amino acid sequences in long proteins like the protein Titin; 2) phonetic sequences of long Russan literary texts (for checking of thoughts of many authors that phonetic organization of human languages is deeply connected with the genetic language). The topics of the algebraic harmony in living bodies and of the quantum-information approach in biology are discussed.

A cyclic antipodal points of a circle is a pair of points that are the intersection of the circle with a diameter of the circle. A recent proof of Ptolemy’s Theorem, simultaneously in both (i) Euclidean geometry; and (ii) the relativistic model of hyperbolic geometry (which is identified with the Klein model of hyperbolic geometry), motivates in this article the study of four cyclic antipodal points of a circle, ordered arbitrarily counterclockwise. The translation of results from Euclidean geometry into hyperbolic geometry is obtained by means of hyperbolic trigonometry, called gyrotrigonometry, to which Einstein addition gives rise. Formulas that extend the Pythagorean formula in both Euclidean and hyperbolic geometry are obtained as byproducts

Financial time series and other human-driven, non-natural processes are known to exhibit fat-tailed outcome distributions. That is, such processes demonstrate a greater tendency for extreme outcomes than the normal distribution or other natural distributional processes would predict. We examine the mathematical expectation, or simply "expectation," traditionally the probability-weighted outcome, regarded since the seventeenth century as the mathematical definition of "expectation." However, when considering the "expectation" of an individual confronted with a finite sequence of outcomes, particularly existential outcomes (e.g., a trader with a limited time to perform or lose his position in a trading operation), we find this individual "expects" the median terminal outcome over those finite trials, with the classical seventeenth-century definition being the asymptotic limit as trials increase to this. Since such finite-sequence "expectations" often differ in values from the classic one, so do the optimal allocations (e.g., growth-optimal). We examine these for fat-tailed distributions. The focus is on implementation, and the techniques described can be applied to all distributional forms.

We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage of using special functions is their analytic continuation which widens the range of the parameters of the definite integral over which the formula is valid. We give as examples definite integrals of logarithmic functions times a trigonometric function. In various cases these generalizations evaluate to known mathematical constants such as Catalan’s constant and π

The article is devoted to biological models using recurrence sequences, which are connected with the harmonic progression 1, 1/2, …, 1/n, and some cooperative properties of genomes. The harmonic progression is itself one of the recurrence sequences based on the harmonic mean. This progression appears in the hyperbolic rules of oligomer cooperative organization in eukaryotic and prokaryotic genomes. This allows thinking that the harmonic progression is also related to inherited physiological systems, which must be structurally consistent with the genetic coding system for their transmission to descendants and survival in evolution. The harmonic progression is one of historically known mathematical series, whose features were studied by Pythagoras, Leibniz, Newton, Euler, Fourier, Dirichlet, Riemann. It is widely used in many known algorithms and is closely related to some other important mathematical objects, for example, the function of the natural logarithm and harmonic numbers. Accordingly, the article describes the possibilities of using these interrelated mathematical objects to model biological structures, including logarithmic spirals and some other. Modeling inherited spiral configurations seems to be a particularly urgent task, since they are extremely common at all levels of organization of living bodies and, according to Goethe, are lines of life. The principle of a recurrence similarity, that is a special similarity of parts and transformations presented in recurrence sequences of numbers and matrix operators (the scale similarity and scale transformations are only particular cases of such similarity), is considered as one of the key principles of structural organization of living bodies.

The existing segmentation-based scene text detection methods mostly need complicated post-processing, and the post-processing operation is separated from the training process, which greatly reduces the detection performance. The previous method, DBNet successfully simplified post-processing and integrated the post-processing into a segmentation network. However, the training process of the model took a long time for 1200 epochs and the sensitivity to texts of various scales was lacking, leading to some text instances being missed. Considering the above two problems, we design the text detection Network with Binarization of Hyperbolic Tangent(HTBNet). First of all, we propose Binarization of Hyperbolic Tangent (HTB), optimized along with which, the segmentation network can expedite the initial convergent speed by reducing the amount of epochs from 1200 to 600. Because features of different channels in the same scale feature map focus on the information of different regions in the image, to better represent the important features of all objects in the image, we devise the Multi-Scale Channel Attention(MSCA). Meanwhile considering that multi-scale objects in the image cannot be simultaneously detected, we propose a novel module named Fused Module with Channel and Spatial(FMCS), which can fuse the multi-scale feature maps from channel and spatial dimension. Finally we adopt cross entropy as the loss function, which measures the difference between predicted values and ground truths. The experimental results show that HTBNet compared with lightweight models has achieved competitive performance and speed on Total-Text(F-measure:86.0%, FPS:30) and MSRA-TD500 (F-measure:87.5%, FPS:30).

A system of wavelet collocation upwind schemes is constructed for solving hyperbolic conserva-tion laws based on a class of interpolation wavelets. The bias magnitude and symmetry factor are defined to depict the asymmetry of the adopted scaling basis function in wavelet theory. Effects of characteristics of the scaling functions on the schemes are explored based on numerical tests and Fourier analysis. The numerical results reveal that the stability of the constructed scheme is af-fected by the smoothness order, N, and the asymmetry of the scaling function. The dissipation analysis suggests that schemes with Neven have negative dissipation coefficients, leading to unstable behaviors. Only scaling functions with Nodd and bias magnitude of 1 can be used to construct stable upwind schemes due to the non-negative dissipation coefficients. Resolution of the wavelet scheme tends to the spectral resolution as the order of accuracy of the scheme in-creases.

This study introduces an innovative integration of hyperbolic metamaterials (HMMs) and photonic crystals (PtCs), each possessing unique dispersion properties that effectively manipulate the propagation of light. We present a PtC waveguide consisting of arrays of HMM nanorods, denoted as HMM PtCs. This waveguide configuration enables the realization of a high figure of merit (FOM) nano-sensor. By modifying the refractive indices of the surrounding materials, the PtC waveguide exhibits alterations in absorption and transmission, allowing for the detection of temperature, pressure, and material variations. Numerical methods were employed to demonstrate the remarkable efficiency of this proposed system, achieving a sensitivity of 324.16 nm/RIU (refractive index unit) and an impressive FOM of 469.58 RIU−1. These results signify a substantial improvement over surface plasmonic sensors, which typically exhibit limited FOMs. As a consequence, the HMM PtC waveguide sensor emerges as an exceptionally appealing option for photonic sensing applications. The proposed HMM PtC waveguide holds vast potential across diverse fields, including biology, medicine, and clinics, representing an exciting advancement for both industry and scientific research.

In this work, we study the dynamical behaviors of the electromagnetic fields and material responses in the hyperbolic metamaterial consisting of periodically arranged metallic and dielectric layers. The thickness of each unit cell is assumed to be much smaller than the wavelength of the electromagnetic waves, so the effective medium concept can be applied. When electromagnetic (EM) fields are present, the responses of the medium in the directions parallel to and perpendicular to the layers are like that of Drude and Lorentz media, respectively. We derive the energy density of the EM fields and the power loss in the effective medium based on Poynting theorem and the dynamical equations of the polarization field. We also show that the Lagrangian density of the system can be constructed. The Euler-Lagrangian equations yield the correct dynamical equations of the electromagnetic fields and the polarization field in the medium. The canonical momentum conjugates to every dynamical field can be derived from the Lagrangian density via differentiation or variation with respect to that field. We apply Legendre transformation to this system, and find that the resultant Hamitonian density is identical to the energy density, up to an irrelevant divergence term.

This work deals with a numerical implementation of a fifth order CENTRAL WENO-TVD (\textit{Weighted Essentially Non-Oscillatory-Total Variation Dimimishing}) of Haschem (2006) scheme applied to the convective terms of some hyperbolic conservation laws problems, in a volume finite framework. The WENO-TVD scheme is used to solve the 1D advection and Burgers equations. For this case is implemented two different numerical fluxes: The Lax-Friedrichs and TVD fluxes. In the TVD fluxes the schemes applied are in flux-limiter form. The schemes implemented for this flux are: Van Albada-1 (van Albada et al.,1982), van Albada-2 (Kermani et al., 2003), van Leer (Hassanzadeh, 2009) and MINMOD (Hirsch, 2007). The WENO type schemes are characterized for their high order approximation, and do not produce spurious oscilations near discontinuities, shocks and higher gradients. A third order Runge-Kutta TVD for the temporal variable is used. Qualitative and quantitative comparison are presented. The numerical solutions are computed with an in-house computer code developed in MATLAB software. In future works, it will develope a paralelization of computer code for solving systems of conservation laws, e.g. Euler equations of gas dynamics.

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

The Chromogranin A (CgA)-derived peptide Catestatin (CST: hCgA352-372) is highly conserved (>90% in 90% species) in mammalian species. The highest-evolved primates show 58.8% similarity with the lowest-evolved monotremes. CST was initially identified as a physiological brake in catecholamine secretion by inhibiting nicotinic-cholinergic signaling. CST also inhibits desensitization of catecholamine secretion, indicating that CST can act both as a cholinergic antagonist (short-term) and as a cholinergic agonist (long-term). The long-term effect sustains catecholamine secretion during stressful situations. CST is now established as a pleiotropic hormone: it affects the cardiovascular system by lowering blood pressure and cardiac contractility, enhancing baroreflex sensitivity, increasing heart rate variability, and promoting angiogenesis; and it increases insulin sensitivity by reducing inflammation, inhibiting hepatic glucose production, attenuating endoplasmic reticulum stress, and inducing glycogen production. The present review will highlight the important direct and indirect effects of CST, CST1-15 (aka cateslytin), D-CST1-15 (where L-amino acids were changed to D-amino acids), and human variants of CST (Gly364Ser-CST and Pro370Leu-CST) on microbial growth inhibition and their potential as therapy for antibiotic-resistant pathogenic microbes.

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 allosteric SERCA (Sarcoplasmic/Endoplasmic Reticulum Ca2+-ATPase) activator CDN1163 has been recently added to the group of pharmacological tools for probing SERCA function. We chose to investigate the effects of the compound on T lymphocyte Ca2+ stores, using the well-described Jurkat T lymphocyte as a reliable cell system for Ca2+ signaling pathways. Our study identified the lowest concentrations of the SERCA inhibitors thapsigargin (TG) and 2,5-di-(tert butyl)-1,4-benzohydroquinone (tBHQ) capable of releasing Ca2+, permitting the differentiation of the TG-sensitive SERCA 2b Ca2+ store from the tBHQ-sensitive SERCA 3 Ca2+ store. We proceeded to test the effects of CDN1163 on Ca2+ stores, examining specific actions on the SERCA 2b and SERCA 3 Ca2+ pools using our low dose SERCA blocker regimen. In contrast to previous work, we find CDN1163 exerts complex time-sensitive and SERCA isoform-specific actions on Ca2+ stores. Surprisingly, short-term exposure (0-30 minutes) to CDN1163 perturbs T cell Ca2+ stores by suppressing Ca2+ uptake with diminished Ca2+ release from the SERCA 2b-controlled store. Concomitantly, we find evidence for a SERCA-activating effect of CDN1163 on the SERCA 3 regulated store, given the observation of increased Ca2+ release inducible by low dose tBHQ. Intriguingly, longer-term (&gt;12 hours) CDN1163 exposure reversed this pattern, with increased Ca2+ release from SERCA 2b-regulated pools, yet decreased Ca2+ release responses from tBHQ-sensitive SERCA 3 pool. Our results reveal differential effects of CDN1163 on Ca2+ stores regulated by distinct SERCA isoforms, prompting the need for careful interpretation of the compound’s effects, particularly in cells expressing multiple SERCA isoforms.

In the paper, the authors consider the generating functions of the Hermite polynomials and their squares, present explicit formulas for higher order derivatives of the generating functions of the Hermite polynomials and their squares, which can be viewed as ordinary differential equations or derivative polynomials, find differential equations that the generating functions of the Hermite polynomials and their squares satisfy, and derive explicit formulas and recurrence relations for the Hermite polynomials and their squares.

With the rapid development of network science, Turing pattern on complex networks has attracted extensive attention from researchers. In this paper, we focus on spatial patterns in multiplex ER (Erdös-Rényi) random networks, taking the predator-prey model with Allee effect and hyperbolic mortality as an example. In theory, the threshold condition for generating Turing pattern is given using the Turing instability theory of multiplex networks. Numerically, we design relevant experiments to explore the impact of network topology on Turing pattern. The factors considered include model parameters, diffusion rate, average degree of the network, and differences in the average degree of different layers. The results indicate that the importance of diffusion rate and network average degree for Turing pattern is affirmed on the single-layer network. For multiplex networks, the differentiation of average degrees in different layers controls the generation of Turing pattern, which is not affected by the diffusion rates of the two populations. More interestingly, we observe the switching of Turing pattern and spatiotemporal pattern. We believe that these findings contribute to a better understanding of self-organization on complex networks.

The space time fractional Korteweg-de Vries equation, modified Equal Width equation and Benney-Luke Equations are solved by using simple hyperbolic tangent Ansatz method. A simple compatible wave transformation in one dimension is employed to reduce the governing equations to integer ordered ODEs. Then, the ansatz approximation is used to derive exact solutions. Some illustrative examples are presented for some particular choices of parameters and derivative orders.

In this study we introduce the new classes $\mathcal{M}_{\alpha}(\sin)$ and $\mathcal{M}_{\alpha}(\cos)$ of $\alpha$-convex functions associated with sine and cosine functions. Also, we obtain the initial coefficient bounds for the first five coefficients of the functions that belong to these classes. Further, we determine the upper bound of Zalcman functional for the class $\mathcal{M}_{\alpha}(\cos)$ for the case $n=3$, showing that the Zalcman conjecture holds for this value. Moreover, the problem of the Fekete-Szeg\H{o} functional estimate for these classes is studied.

In this paper we give approximations to the Mittag-Leffler functions in terms of elementary functions using different methods. This allowed us to establish a practical method we called integerization principle. This principle states that many fractional nonlinear oscillators may be solved by means of the solution to some integer-order Duffing oscillator equation. The accuracy of the obtained results is illsutrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.

Orthohepadnavirus causes chronic hepatitis in a broad range of mammals, including primates, cats, woodchucks, and bats. Hepatitis B virus (HBV) X protein inhibits type-I interferon (IFN) signaling, promoting HBV escape from the innate immune system to establish persistent infection. However, whether X proteins of Orthohepadnavirus viruses in the other species have similar inhibitory activity remains unknown. Here, we investigated the anti-IFN activity of 17 Orthohepadnavirus X proteins derived from various hosts. We observed conserved activity of Orthohepadnavirus X proteins in inhibiting TIR-domain-containing adaptor protein inducing IFN-β (TRIF)-mediated IFN-β signaling pathway through TRIF degradation. X proteins from domestic cat hepadnavirus (DCH), a novel member of Orthohepadnavirus, inhibited mitochondrial antiviral signaling protein (MAVS)-mediated IFNβ signaling pathway comparable with HBV X. These results indicate that inhibition of IFN signaling is conserved in Orthohepadnavirus X proteins.

Human activities (e.g., exploitation, utilization, and conservation) exert substantial impact on forest ecological functions (FEF). The human influence on FEF significantly varies across developmental stages, which are attributed to the temporal and spatial in nature. This study evaluates some notable FEF indices (FEFI) in the 448 counties within the Yellow River basin (YRB) using panel data from the Seventh to Ninth National Forest Inventory. Data analysis involves employing the residual trends, geographical and temporal weighted regression. Results indicate that, firstly, the overall forest ecological function in the YRB is moderate to inferior, with superior FEF in counties endowed with more natural forest resources. Afforestation demonstrates a short-term improvement, but its effectiveness diminishes over time. Secondly, the positive spatial correlation is stronger among counties, characterized by both high-high and low-low agglomeration effects. Scattered planting, simple stand structure, and concentrated harvesting of forests at the identical stand ages hinder the formation of complex and large-scale FEF agglomerations. Thirdly, significant spatial-temporal differences exist in the impact of human activities on FEF. In the upper reaches of the basin, increased vegetation coverage through agricultural and forestry production benefited FEF, however, some over-exploitation of forests and grasslands is observed there. In the middle reaches, the economic development, expanding population and the greening activities help to improve FEF effectively, but excessive water using in agricultural production brought more difficulties to FEF improvement. In the lower reaches of the basin, improved wastelands and forest protection positively influence FEF. This study recommends that county governments should prioritize forest management with multi-species and multi-layered complex forests. Each county should define its position in regional development and ecological protection, considering the potential impacts on neighboring regions. This holistic approach promotes more effective integrated regional management.

A new set of basis functions is presented. The foundation in mathematics is established. To reconstruct a signal, it is compared to the Fourier basis functions. The M-basis functions' potential applications are also presented.

The developmental phase of adolescence is characterized by a multitude of neurocognitive and psychosocial changes and is therefore considered one of the most critical developmental periods of life. Experimentation on the use of substances often begins in adolescence and so does the addiction process. Most research in human subjects shows that chronic cannabis abuse is the cause of the impairment of some cognitive functions, affecting the performance on divided attention, verbal memory and working memory. In this study, we wanted to investigate how the abuse of cannabis (chronic, occasional and absence use) can influence global cognitive functioning, also through executive functions. From the statistical analyzes of our study, it emerges that the group of subjects who use chronic cannabis (group 1) has a significant drop in working memory tasks compared to the group that does not use it (group 3). In addition, the goal of future studies by our group is to verify the permanent alteration of cognitive processes affected through revaluations with calendar follow-up (controlled).

We show that if $f$ is a non-negative superquadratic function, then $A\mapsto\mathrm{Tr}f(A)$ is a superquadratic function on the matrix algebra. In particular, \begin{align*} \tr f\left( {\frac{{A + B}}{2}} \right) +\tr f\left(\left| {\frac{{A - B}}{2}}\right|\right) \leq \frac{{\tr {f\left( A \right)} + \tr {f\left( B \right)} }}{2} \end{align*} holds for all positive matrices $A,B$. In addition, we present a Klein's inequality for superquadratic functions as $$ \mathrm{Tr}[f(A)-f(B)-(A-B)f'(B)]\geq \mathrm{Tr}[f(|A-B|)] $$ for all positive matrices $A,B$. It gives in particular improvement of Klein's inequality for non-negative convex function. As a consequence, some variants of the Jensen trace inequality for superquadratic functions have been presented.

Superantigens are unconventional antigens which recognise immune receptors outside the usual binding sites e.g. complementary determining regions (CDRs), to elicit a response within the target cell. T-cell superantigens crosslink T-cell receptors and MHC Class II molecules on antigen-presenting cells, leading to lymphocyte recruitment, induction of cytokine storms and T-cell anergy or apoptosis among many other effects. B-cell superantigens, on the other hand, bind immunoglobulin receptors on B-cells affecting opsonisation, IgG-mediated phagocytosis, and drive B-cells into apoptosis. Here, through a review of the structural basis for recognition of immune receptors by superantigens, we show that their binding interfaces share specific physicochemical characteristics when compared with other protein-protein interaction complexes. Given that antibody-binding superantigens have been exploited extensively in industrial antibody purification, these observations could facilitate further protein engineering to optimize the use of superantigens in this and other areas of biotechnology.

We consider two abstract systems of parabolic-hyperbolic type that model thermoelastic problems. We study the influence of the physical constants and the initial data on the nonexistence of global solutions that in our framework are produced by the blow-up in finite time of the norm of the solution in the phase space. We employ a differential inequality to find sufficient conditions that produce the blow-up. To that end, we construct a set that is positive invariant for any positive value of the initial energy. As a result we found that the coupling with the parabolic equation stabilizes the system, as well as the damping term in the hyperbolic equation. Moreover, for any pair of positive values $(\xi,\epsilon)$, there exist initial data such that the corresponding solution with initial energy $\xi$ blows-up at a finite time less than $\epsilon$. Our purpose is to improve results previously published in the literature.

Suppose for n∈ ℕ, set A⊆ℝⁿ and function f∶A→ℝⁿ. If set A, using the Hausdorff outer measure, is measurable in the sense of Carathèodory; we want to find an extension of the expected value, w.r.t the Hausdorff measure, that's unique, finite and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. The issue is current extensions of the expected value are finite for all functions in only a shy subset of ℝᴬ. The reason this issue wasn't resolved is mathematicians have not thought of the problem, focusing on application rather than generalization. Despite the lack of potential use, we'll attempt to solve the problem by defining a choice function---this shall choose a unique set of equivalent sequences of sets (Fₖ***) , where the set-theoretic limit of Fₖ*** is the graph of f; the measure Hʰ is the ℎ-Hausdorff measure, such for each k∈ℕ, 0 < Hʰ(Fₖ***) < +∞; and (fₖ*) is a sequence of functions where {(x,fₖ*(x))∶x∈ dom(Fₖ***)}=Fₖ***. Thus, the extended expected value of or E**[f,Fₖ***] is: ∀(ε>0)∃(N∈ℕ)∀(k∈N)(k≥N⇒1/Hʰ(dom(Fₖ***))∫dom(Fₖ*** )fₖ* dHʰ - E**[f,Fₖ***]<ε ) which should be unique, finite, and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. Note we guessed the choice function using computer programming but we don’t use mathematical proofs due to the lack of expertise in the subject matter. Despite this, the biggest use of this research is the extension of the expected value is finite for "almost all" functions: this is easier to use in application when finding the "average" of functions covering an infinite expanse of space.

Executive functions comprise top-down cognitive processes that exert control over information processing, from acquiring information to issuing a behavioural response. These cognitive processes of inhibition, working memory and shifting underpin complex cognitive skills, such as episodic memory and planning, which have been repeatedly investigated in several bird species in recent decades. Until recently, avian executive functions were studied in relatively few bird species, but have gained traction in comparative cognitive research following MacLean and colleagues’ large-scale study (2014). Therefore, in this review paper, relevant previous findings are collected and organized to facilitate further investigations of these core cognitive processes in birds. This review can assist in integrating findings from avian and mammalian cognitive research and further current understanding of executive functions’ significance and evolution.

In the paper, by convolution theorem for the Laplace transforms and analytic techniques, the author finds necessary and sufficient conditions for complete monotonicity, monotonicity, and inequalities of several functions involving polygamma functions. By these results, the author derives a lower bound of a function related to the sectional curvature of the manifold of the beta distributions. Finally, the author poses several guesses and open problems related to monotonicity, complete monotonicity, and inequalities of several functions involving polygamma functions.

Sparse training (ST) aims to ameliorate deep learning by replacing fully connected artificial neural networks (ANNs) with sparse or ultra-sparse ones, such as brain networks are, therefore it might benefit to borrow brain-inspired learning paradigms from complex network intelligence theory. Here, we launch the ultrasparse advantage challenge, whose goal is to offer evidence on the extent to which ultra-sparse (around 1% connection retained) topologies can achieve any leaning advantage on fully connected. Epitopological learning is a field of network science and complex network intelligence that studies how to implement learning on complex networks by changing the shape of their connectivity structure (epitopological plasticity). One way to implement Epitopological (epi- means new) Learning is via link prediction: predicting the likelihood of nonobserved links to appear in the network. Cannistraci-Hebb learning theory inspired the CH3-L3 network automata rule for link prediction which is effective for general-purpose link prediction. Here, starting from CH3-L3 we propose Epitopological Sparse Meta-deep Learning (ESML) to apply Epitopological Learning to sparse training. In empirical experiments, we find that ESML learns ANNs with ultra-sparse hyperbolic (epi-)topology in which emerges a community layer organization that is meta-deep (meaning that each layer also has an internal depth due to powerlaw node hierarchy). Furthermore, we discover that ESML can in many cases automatically sparse the neurons during training (arriving even to 30% neurons left in hidden layers), this process of node dynamic removal is called percolation. Starting from this network science evidence, we design Cannistraci-Hebb training (CHT), a 4-step training methodology that put ESML at its heart. We conduct experiments on 6 datasets and 3 network structures (MLPs, VGG16, ResNet50) comparing CHT to dynamic sparse training SOTA algorithms and fully connected network. The results indicate that, with a mere 1% of links retained during training, CHT surpasses fully connected networks on VGG16 and ResNet50. This key finding is an evidence for ultra-sparse advantage and signs a milestone in deep learning. CHT acts akin to a gradient-free oracle which adopts CH3-L3 based epitopological learning to guide the placement of new links in the ultra-sparse network topology to facilitate sparse-weight gradient learning, and this in turn reduces the convergence time of ultra-sparse training. Finally, CHT offers first examples of parsimony dynamic sparse training because, in many datasets, it canretain network performance by percolating and significantly reducing the node network size.

The main objective of this paper is to introduce a further extension of extended (p, q)-beta function by considering two Mittag-Leffler function in the kernel. We investigate various properties of this newly defined beta function such as integral representations, summation formulas and Mellin transform. We define extended beta distribution and its mean, variance and moment generating function with the help of extension of beta function. Also, we establish an extension of extended (p, q)-hypergeometric and (p, q)-confluent hypergeometric functions by using the extension of beta function. Various properties of newly defined extended hypergeometric and confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are investigated.

In this paper, we relate Poisson’s summation formula to Heisenberg’s uncertainty principle. They both express Fourier dualities within the space of tempered distributions and these dualities are furthermore the inverses of one another. While Poisson’s summation formula expresses a duality between discretization and periodization, Heisenberg’s uncertainty principle expresses a duality between regularization and localization. We define regularization and localization on generalized functions and show that the Fourier transform of regular functions are local functions and, vice versa, the Fourier transform of local functions are regular functions.

Abstract: Remarkably, the p53 transcription factor, referred to as “the guardian of the genome”, is not essential for mammalian development. Moreover, efforts to identify p53‑dependent developmental events have produced contradictory conclusions. Given the importance of pluripotent stem cells as models of mammalian development, and their applications in regenerative medicine and disease, resolving these conflicts is essential. Here we attempt to reconcile disparate data into justifiable conclusions predicated on reports that p53‑dependent transcription is first detected in late mouse blastocysts, that p53 activity first becomes potentially lethal during gastrulation, and that apoptosis does not depend on p53. Furthermore, p53 does not regulate expression of genes required for pluripotency in embryonic stem cells (ESCs); it contributes to ESC genomic stability and differentiation. Depending on conditions, p53 accelerates initiation of apoptosis in ESCs in response to DNA damage, but cell cycle arrest as well as the rate and extent of apoptosis in ESCs are p53-independent. In embryonic fibroblasts, p53 induces cell cycle arrest to allow repair of DNA damage, and cell senescence to prevent proliferation of cells with extensive damage.

This paper deals with the analysis of the cognitive functions of the cerebral cortex or cortex in the evolutionary context. The triune brain model is presented given its notorious popularity in fields that are not strictly neuroscientific, and its limitations and inaccuracies are also shown. Although it is an outdated theory, this one represented the passage to a new era, because it really was the model of the movement towards understanding the brain in evolutionary terms. Next, the paper illustrates the different areas of the cortex and their functions, as well as the evolution of the brain and the cortex in vertebrates. To date, the expansion of the cortex with the amniotes was placed 300 million years ago, although recent studies place it in the lampreys more than 500 million years ago. Evolutionary changes in mammalian brain and cortex size are discussed, showing the evolution from three to six cell layers and trends in different groups of mammals. Finally, the most recent contributions in the field of research are illustrated, such as the role of neurogenesis and the evolution of the connectivity of the cortex.

TThis paper delves into the extension and characterization of radial positive definite functions into non-integer dimensions. We provide a thorough investigation by employing the Riemann-Liouville fractional integral and fractional Caputo derivatives, enabling a comprehensive understanding of these functions. Additionally, we introduce a secondary characterization based on the Bernstein characterization of completely monotone functions. The practical significance of our study is showcased through an examination of the positivity of the fundamental solution of the space-fractional Bessel diffusion equation, highlighting the real-world applicability of the developed concepts. Through this work, we contribute to the broader understanding of radial positive definite functions and their utility in diverse mathematical and applied contexts.

Natural cycles underpin the very stuff of life. In this commentary we consider unnatural cycles: that is, anthropogenic activities which have a circularity, but whose nature is to have a detrimental effect on human health, exacerbating existing problems. Natural cycles have feedback loops, some of which have recently come to light, with an understanding that everything is connected in some way. In health, feedback loops are imperative in homeostatic mechanisms. However, in the unnatural cycle the feedback loops serve to reinforce (and in some cases amplify) negative problems. We offer a commentary on an unnatural cycle moving from air quality to lung function and back to air quality; we call this the lung disease unnatural cycle. We suggest where links occur, and where wider consideration of interactions between various disciplines can lead to breaking this unnatural (or vicious) cycle, changing it to a healthy cycle where individual health can be improved, along with better global scale outcomes. We suggest that many activities within this unnatural cycle occur within silos. However, the improved cycle incorporates joint activities at geological, health, and financial levels, to the mutual benefit of all, breaking the unnatural cycle, and improving health, life and financial costs.

In this review we summarize the recent development in understanding the role of PIP2 in cellular function and signaling. We first discuss the effect of PIP2 on actin binding proteins addressing the mechanism of the actin cytoskeletal dynamics such as polymerization or depolymerization of the filamentous network or the coupling to membrane to generate forces. Next, we outline the role of PIP2 in membrane dynamics. We summarized how the membrane organization depends upon PIP2 in the presence of ions or transmembrane proteins that are sensitive to membrane curvature. We discuss how clathrin coated pits interact with adaptor proteins during the endocytosis process, which is facilitated by PIP2. Finally, we discuss the role of PIP2 in cell signaling and diseases.

In numerous instances, the fate of a single cell not only represents its peculiar outcome but also contributes to the overall status of an organism. In turn, cell division cycle and its control strongly influence cell destiny playing a critical role in targeting it towards a specific phenotype. Several factors participate to the control of growth and among them p27 and p57, two proteins modulating various transitions of cell cycle, appear to play key functions. In this review, the major features of p27 and p57 will be described, focusing in particular on their recently identified roles not directly correlated to cell cycle modulation. Then, their possible role as molecular effectors of polyphenols activities are discussed. Polyphenols represent a large family of natural bioactive molecules that have been demonstrated to play promising protective activities against several human diseases. Their use has also been proposed in association with classical therapies for ameliorating their clinical effects and for diminishing their negative side activities. The importance of p27 and p57 in polyphenol cellular effects will be discussed with the aim of identifying novel therapeutic strategies for the treatment of important human diseases, such as cancers, characterized by an altered control of growth.

The comparison of group means in latent variable models plays a vital role in empirical research in the social sciences. The present article discusses extensions of invariance alignment and Haberman linking concerning the choice of linking functions for comparisons of many groups. Robust linking functions are proposed for invariance alignment and robust Haberman linking that are particularly suited to item response data under partial invariance. In a simulation study, it is shown that both linking approaches have comparable performance, and in some conditions, the newly proposed robust Haberman linking outperforms invariance alignment.

A new generalization of extended beta function and its various properties, integral representations and distribution are given in this paper. In addition, we establish the generalization of extended hypergeometric and con uent hypergeometric functions using the newly extended beta function. The properties these extended and con uent hypergeometric functions such as integral representations, Mellin transformations, dif- ferentiation formulas, transformation and summation formulas are also investigated.

In a recent paper, Sarikaya et al. introduced a new analogue of the classical Gamma function which they called, the conformable Gamma function. Motivated by their results, this paper seeks to establish some inequalities for the conformable Gamma and Polygamma functions. Among other analytical tools, the procedure relies on the generalized forms of some classical inequalities.

A general methodology for loan amortization under arbitrary discount functions is discussed. It is shown that it is always possible to uniquely define a scheme for constructing the loan amortization schedule with an arbitrary assigned discount function. It is also shown that even if the loan amortization is carried out from the sequence of principal payments and the sequence of accrued interest, the underlying discount function can be uniquely determined at the maturities corresponding to the installment payment dates. As a special case of the proposed approach, we derive the amortization method according to the law of simple interest.

A system to evaluate several facets of hand function for neuroprostheses-mediated tasks is proposed. It includes a platform that serves as a test bench, sensors for dynamometry, electromyography, sensorized glove, and interactive objects. The system methodically locates and assesses the motor points along the forearm, evaluates stimulation-induced fatigue, measures digit motion and forces exerted during ADL grasps, and evaluates nerve excitability to advance electrode designs. While the system is exclusively designed for neuroprostheses-mediated grasp, it can also be extended to generic grasp and object manipulation-based research.

We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting capital allocation gives a way to divide the surplus between the insured and the capital providers, i.e. the shareholders.

CX3CL1, also named fractalkine or neurotactin, the only known member of the CX3C chemokine family that can chemoattract several immune cells. CX3CL1 exists in both membrane-anchored and soluble forms, each mediating distinct biological activities. CX3CL1 signals are transmitted through its unique receptor, CX3CR1, primarily expressed in microglia of central nervous system (CNS). In the CNS, CX3CL1 acts as a regulator of microglia activation in response to brain disorders or inflammation. Recently, there has been a growing interest in the roles of CX3CL1 in regulating cell adhesion, chemotaxis, and host immune response in viral infection. Here, we provide a comprehensive review of the changes and function of CX3CL1 in various viral infections such as human immunodeficiency virus (HIV), SARS-CoV-2, influenza virus and cytomegalovirus (CMV) infection, to highlight the emerging roles of CX3CL1 in viral infection and the associated diseases.

Cognitive functions are based on neuronal plasticity, which is provided by various mechanisms involving numerous bioactive molecules, the most important of which are endocannabinoids (eCBs). Over the past three decades, a lot of data have been accumulated on the involvement of eCBs in the mechanisms of memory and other cognitive functions. These functions are impaired in neurodegenerative diseases such as Alzheimer's disease (AD) and temporal lobe epilepsy (TLE). The main pathological feature of neurons in AD and TLE is increased excitability; therefore, an activation of the endocannabinoid system, which controls cellular excitation, may be a promising approach in their therapy. The available information about the effect of (endo)cannabinoids on cognitive functions is contradictory, which may depend on the drugs used, their dose, and the experimental conditions. There is an extensive literature indicating a protective effect of cannabinoids in the treatment of neurodegenerative diseases in humans and in animal models of cognitive deficits. This review, focusing on the recent researches, is devoted to the analysis of the effects of endocannabinoid system activation on cognitive functions in norm and in the brain with neurodegeneration that occurs in AD and TLE diseases. Possible reasons for inconsistencies in the available data are discussed.

NSD3 is a member of the NSD histone methyltransferase family of proteins. In recent years, it has been identified as a potential oncogene in certain types of cancer. NSD3 gene encodes three isoforms, the full length, a short (NSD3S) and WHISTLE isoforms. Importantly, NSD3S isoform corresponds to the N-terminal of the full-length protein, lacking the methyltransferase domain. The chromosomal location of NSD3 is frequently amplified across cancer types, such as breast, lung, colon, among others. Recently, this amplification has been correlated to a chromothripsis event, that could explain the different NSD3 alterations found in cancer. Fusion proteins containing NSD3 have also been reported, such as leukemia NSD3-NUP98, and in NUT midline carcinoma (NMC), NSD3-NUT fusion. Its role as an oncogene has been described by modulating different cancer pathways through its methyltransferase activity, or the short isoform of the protein, through protein interactions. Specifically, in this review we will focus on stating the functions that have been characterized as methyltransferase dependent, and those that have been correlated with the expression of the NSD3S isoform. Altogether, there is evidence that both isoforms of NSD3 are relevant for cancer progression, establishing NSD3 as a therapeutic target. However, further functional studies are needed to differentiate NSD3 oncogenic activity as dependent or independent of the catalytic domain of the protein, as well as the contribution of each isoform and its clinical significance in cancer progression.

In this paper we consider the congruence problem that arises in the post-analysis of Bayesian network models reconstructed from different datasets. Apart from the structure, a typical network numerically encodes relationship intensities, assigning numerical score to network edges via the scoring criterion used in the reconstruction process. This scoring is rarely a directly interpretable quantity with proper units of measure and an absolute scale, and often comes short in desirable characteristics of a true metric. This leads to poor portability of edge magnitude considerations between similar networks, originating from different sources. In this work, we address this problem by estimating the effect that data-specific resolution limit has on conditional independence, as reflected by information-theoretic entropy, and by the appropriate modification of MDL score, which removes the inconsistency between the score components in both the meaning and units. We also numerically validate our findings and expose additional performance advantages obtained via this modification.

Current therapeutic strategies targeting cancer cells within solid tumors have displayed limited success owing to the presence of non-cancer components referred to as the tumor stroma within the tumor microenvironment (TM). These stromal cells, extracellular matrix and blood vessels influence cancer cell response to therapy and play key roles in tumor relapse and resistance. Of the stromal cells present in the TM, a lot of attention has been given to cancer-associated fibroblasts (CAFs) as they are the most abundant and are important in cancer initiation, progression and therapy resistance. In this updated review I emphasize the role of CAFs in the regulation of tumor cell behaviour and reveal how CAF-derived factors and signaling influence tumor cell heterogeneity and development of novel strategies to combat cancer. To investigate the expression of CAF markers in tumor tissues versus normal tissues, transcriptomic data from The Cancer Genome Atlas (TCGA) and the Gene Expression Profiling Interactive Analysis (GEPIA) databases was used. Bioinformatic analysis reveals differential expression of CAF markers in several cancer types, underscoring the need for further multiomics and biochemical studies on CAFs, CAF subsets and markers. Differences in CAF markers’ expression could be due to different cellular origins as well as the effect of cancer-specific tumor microenvironmental effect on CAFs. Lastly, I present recent advances in therapeutic targeting of CAFs and the success of such endeavours or its lack thereof. It is recommended that for patients’ outcomes to improve, cancer treatment be combinatorial in nature, targeting both cancer cells and stromal cells and interactions.

The aim of this paper is to identify and document some functions and contextsof traditional pottery within northern Ghana. The descriptive approach of the qualitative research methodology was employed. Interview and observation methods were employed as the data collection methods. They were used to ascertain reasons why some potteryare engaged in certain contexts andfor certainfunctions. The data was tabulated to include the traditional name of the pot, the function and the context. The data were then analyzed and the indications were that, the potters make interesting forms of traditional pottery for different purposes; and the local name given to each pot perfectly defines their functions and contexts within northern Ghana. On the flipside of the coin, the function and context of every pot can also be dictated by its end user. Base on this, the researchers were able to discover some functions and contexts of the indigenous pottery which were put into some groups. On the first hand, the researchers classified the functions into five groups of purpose. These included: domestic purposes, religious purposes, agricultural purposes, rites of passage purposes and traditional herbal medicinal purposes. On other hand, seven groups of contexts were also discovered at the time of the study. These included: courtyards, bedrooms, bathrooms, graveyards, kitchens, shrines, and hencoops as places where these pots can be found among the people of the Northern Ghana.

In this article, we present two topics related to mathematical economics. We offer an intriguing proposal for securing cost and production functions in the face of uncertainty and risk. We discuss the relationship between individual and social preferences. This is important because traditional revealed preference theory does not account for such factors.

Individuals and their leadership competencies have been the sole focus of project leadership research, rather than the project leadership's behaviour and functions in project and organizational settings. As a result, this study investigates the project leadership functions and behaviours required for various project and organizational situations in order to propose a project leadership model that will be effective in all project and organizational situations. The model that was developed and tested in this study theorized on the project leadership function that project leaders are expected to perform as a result of their positions. It also described how project leaders could tailor their leadership functions and behaviours to address issues related to positions, organizational situations, and project situations. Three hypotheses were developed and tested using structural equation modelling to validate the model. The model's perceptive power demonstrates adequate validity. The model's validity implies that there are appropriate project leadership functions for different leadership levels and circumstances. The model's validity also implies that each project leadership behaviour has its own value, as conditions and necessities dictate. The study assumes that a project leader can embrace project leadership by combining a few different project leadership functions and behaviours.

This paper introduces extensions H4,p and X8,p of Horn’s double hypergeometric function H4 and Exton’s triple hypergeometric function X8, taking into account recent extensions of Euler’s beta function, hypergeometric function, and confluent hypergeometric function. Among the numerous extended hypergeometric functions, the primary rationale for choosing H4 and X8 is their comparable extension type. Next, we present various integral representations of Euler and Laplace type, Mellin and inverse Mellin transforms, Laguerre polynomial representation, transformation formulae and a recurrence relation for the extended functions. In particular, we provide a generating function for the X8,p and several bounding inequalities for the H4,p and X8,p.

The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its extensive use in optics, engineering, and signal processing. In the present work, we aimed to expand the fractional Hilbert transform to a space of generalized functions known as Boehmians. We introduce a new fractional convolution operator for the fractional Hilbert transform to prove a convolution theorem similar to the classical Hilbert transform and also to extend the fractional Hilbert transform to Boehmians. We also construct a suitable Boehmian space on which the fractional Hilbert transform exists. Further, we investigate convergence of the fractional Hilbert transform for the class of Boehmians and discuss the continuity of the extended fractional Hilbert transform.

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

Three-dimensional transfer functions (3D TFs) are generally assumed to fully describe the transfer behavior of optical topography measuring instruments such as coherence scanning interferometers in the spatial frequency domain. Therefore, 3D TFs are supposed to be independent of the surface under investigation resulting in a clear separation of surface properties and transfer characteristics. In this paper we show that the 3D TF of an interference microscope differs depending on whether the object is specularly reflecting or consists of point scatterers. In addition to the 3D TF of a point scatterer, we will derive an analytical expression for the 3D TF corresponding to specular surfaces and demonstrate this as being most relevant in practical applications of coherence scanning interferometry (CSI). We additionally study the effects of temporal coherence and disclose, that in conventional CSI temporal coherence effects dominate. However, narrowband light sources are advantageous if high spatial frequency components of weak phase objects are to be resolved, whereas for low-frequency phase objects of higher amplitude the temporal coherence is less affecting. Finally, we present an approach that explains the different transfer characteristics of coherence peak and phase detection in CSI signal analysis.

GIGANTEA (GI) is a gene involved in multiple biological functions, which were analysed and are partially conserved in a series of mono- and dicotyledonous plant species. The identified biological functions include control over the circadian rhythm, light signalling, cold tolerance, hormone signalling and photoperiodic flowering. The latter function is a central role of GI, as it involves a multitude of pathways, both dependent and independent of the gene CONSTANS(CO) as well as on the basis of interaction with miRNA. The complexity of gene function of GI increases due to the existence of paralogs showing changes in genome structure as well as incidences of sub- and neofunctionalization. We present an updated report of the biological function of GI, integrating late insights into its role in floral initiation, flower development and flower volatile production.

Many complex behaviours in biological systems emerge from large populations of interacting molecules or cells, generating functions that go beyond the capabilities of the individual parts. Such collective phenomena are of great interest to bioengineers due to their robustness and scalability. However, engineering emergent collective functions is difficult because they arise as a consequence of complex multi-level feedback, which often spans multiple length-scales. Here, we present a perspective on how some of these challenges could be overcome by using multi-agent modelling as a design framework within synthetic biology. Using case studies covering the construction of synthetic ecologies to biological computation and synthetic cellularity, we show how multi-agent modelling can capture the core features of complex multi-scale systems and provide novel insights into the underlying mechanisms which guide emergent functionalities across scales. The ability to unravel design rules underpinning these behaviours offers a means to take synthetic biology beyond single molecules or cells and towards the creation of systems with functions that can only emerge from collectives at multiple scales.

In this work, an operator superquadratic function (in operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed out. Equivalent statements of a non-commutative version of Jensen's inequality for operator superquadratic function are established. A generalization of the main result to any positive unital linear map is also provided.

Some refinements and reverses of the Fejer's inequality for convex functions are given.

Partial sums of analytic univalent functions and partial sums of starlike have been investigated extensively by several researchers. In this paper, we investigate a partial sums of convex harmonic functions that are univalent and sense preserving in the open unit disk.

Tight junctions (TJ) are cell-cell adhesive structures that define the permeability of barrier-forming epithelia and endothelia. In contrast to this seemingly static function, TJs display a surprisingly high molecular complexity and an unexpected dynamic regulation, which allows the TJs to maintain a barrier in the presence of physiological forces and in response to perturbations. Cell-cell adhesion receptors play key roles during the dynamic regulation of TJs. They connect individual cells within cellular sheets and link sites of cell-cell contacts to the underlying actin cytoskeleton. Recent findings support roles of adhesion receptors in transmitting mechanical forces and promoting phase separation. In this review, we discuss newly discovered functions of cell adhesion receptors localized at the TJs and their role in the regulation of the barrier function.

Carbon dots are carbon based nanoparticles, which have the characteristics of simple preparation process, photoluminescence, biocompatibility, adjustable surface function, water solubility, and low toxicity. They are widely used in biological applications such as imaging, biosensing, photocatalysis, and molecular transfer. It has also aroused great interest among researchers in agriculture and has made significant progress in improving crop growth and production. This review presents the physiological functions of carbon dots for crop growth and development, photosynthesis, water and nutrient absorption, and abiotic stress resistance and their applications in improving ecological environment and agriculture as biosensors, and the future application prospects and research directions of carbon dots in agriculture were prospected.

The paper investigates new robust code constructions based on bent functions and spline–wavelet transformation. Implementation of bent functions in codes construction increases the probability of error detection in the data channel and cryptographic devices. Meanwhile, use of spline–wavelets theory for constructing the codes gives the possibility to increase system security from the actions of an attacker. Presented constructions combines spline–wavelets functions and bent functions. Developed robust codes, compared to existing ones, have a higher parameter of maximum error masking probability. Illustrated codes are ensuring the security of transmitted information. Some of the granted constructions were implemented on FPGA.

The time symmetry of T_c = CT is redefined based on the 4-D Euclidean space. The time inversion symmetry of T_c = CT changes the signs of the charge (q) and absolute time (ct) of the particle. The P symmetry changes the signs of the space momenta and handedness of the particle. The T_c symmetry changes the signs of the time momentum (P_t=E/c) and charges. The handedness are classified as the left-handedness and right-handedness on the 3-D space. The charges (|q| = cDt) and energies (E= cDtDV) of the particles are originated from the upward warping (q>0) and downward warping (q<0) of the particles along the time axis. The evolution of our matter universe with P_t > 0 since the big bang can be interpreted based on the CTP symmetry with the partner antimatter universe with p_t < 0. The photon space is called as the vacuum space. Then the E and M waves are the space fluctuations, and the gravitational G wave is the time fluctuations. And the E, M and G fields are newly explained. The zero E and M fields of the photon space indicates that the photon space and gamma ray are the 2EM waves. The rest mass energy of the particle is the 4-D space volume of the warped photon space. In the present work, the quantum wave function is considered as the 4-D vector with the space wave function and time axis wave function in the 4-D Euclidean space. The warped photon space corresponds to the squared wave function which is the probability density. It is concluded that, in the quantum mechanics, the imaginary number concept is introduced in the quantum wave functions instead of the time axis component of the 4-D wave function vector. The left-handed neutrino puzzle is explained from the handedness partner relation with the right-handed dark matters. Finally, the modified Lorentz transformations derived in the 4-D Euclidean space are compared with the Lorentz transformations of the special and general relativity theories in the 4-D Minkowski space.

Chemokine C-C receptor 6 (CCR6) and its exclusive ligand CCL20 is an extremely important chemokine receptor-ligand pair which controls cell migration and immune induction during inflammatory disease. Not many scientific studies have been undertaken to study its immune mechanisms in detail, but its unique contribution to steady state cell chemotaxis in upholding immune tolerance and regulating immune homeostasis during inflammation is evident in multiple organ systems, including lung, liver, kidney, skin, brain, eye, joints, gonads and the gut in the human body. The role of CCR6 is constitutively expressed as a series of much debilitating severe inflammatory and autoimmune diseases, HIV and cancer metastasis. CD4⁺ T cells, the central organizers of adaptive immunity, are stringently mobilized by the CCR6/CCL20 axis also induced by cytokines and a host of other factors in a carefully executed immune modulation scenario, to bring about a delicate balance between pro-inflammatory T_H17 cells and regulatory T_reg cells. Although the exact immune regulatory role is not elucidated yet, CCR6/CCL20 axis is implicated as a front runner which determines the polarization of T_H17 and T_reg cells and consequently the resolution or progression of many debilitating disorders. This review therefore aims at emphasizing the pleiotropic significance of the chemokines CCR6 and CCL20 in immunologic function in multiple organ systems thereby hoping to accentuate its value in future therapeutic modalities.

In this work we study the energy consumption by various modern secured hash functions (MD2, MD5, SHA-1, and SHA-2) and modern symmetric key encryption protocols (Blowfish, DES, 3DES, and AES) from the algorithmic perspective. We identify various parameters that moderate energy consumption of these hashes and protocols. Our work is directed towards redesigning or modifying these algorithms to make them consume lesser energy. As a first step, we try to determine the applicability of the asymptotic energy complexity model by Roy et. al. on these hashes and protocols. Specifically, we try to observe whether parallelizing the access of blocks of data in these algorithms reduces their energy consumption based on the energy model. Our results confirm the applicability of the energy model on these hashes and protocols. Our work is motivated by the relevance and importance of cryptographic hashes and symmetric key protocols for modern ICT (Information and Communication Technology), and ICT enabled industry to keep them protected from dynamically changing threat scenarios. Hence the design of more energy efficient hashes and protocols will definitely contribute in reducing the ICT energy consumption that is continuously increasing.

Knowledge of the agricultural soil microbiota, of the microbial consortia that comprise it, and the promotion of agricultural practices that maintain and encourage them, is a promising way to improve soil quality for sustainable agriculture and to provide food security. Although numerous studies have demonstrated the positive effects of beneficial soil microorganisms on crop yields and quality, the use of microbial consortia in agriculture remains low. Microbial consortia have more properties than an individual microbial inoculum, due to the synergy of the microorganisms that make them up. This review describes the main characteristics, ecosystem functions, crop benefits and biotechnological applications of microbial consortia composed of arbuscular mycorrhizal fungi, plant growth promoting bacteria and actinobacteria, to promote the restoration of agricultural soils and, consequently, the quality and health of agricultural crops. The aim is to provide knowledge that will contribute to the development of sustainable and sufficiently productive agriculture, which will adapt in a good way to the pace of the growing human population and to climate change.

In this work, several inequalities of Popoviciu type for h-MN-convex functions are proved, where M and N are denote to Arithmetic, Geometric and Harmonic means and h is a non-negative superadditive or subadditive function.

2,4-dichlorophenoxyacetic acid (2,4-D) is a globally used herbicide and is frequently found in water samples. This fact has prompted studies on its effects in non-target organisms, revealing significant alterations on liver structure and function. In this review, we evaluated the literature on the hepatotoxicity of 2,4-D, focusing on morphological damages, biomarkers of toxicity and affected liver functions. Searches were conducted on PubMed, Web of Science and Scopus and 83 articles were selected after curation. Among the studies, 72% used in vivo models and 30% used in vitro models. Additionally, 48% used the active ingredient, and 35% used commercial formu-lations in exposure experiments. The most affected biomarkers were related to a decrease in an-tioxidant capacity, including alterations in the activities of catalase and superoxide dismutase, and in the levels of malondialdehyde. Changes in energy metabolism, lipids, liver function, and xenobiotic metabolism were also identified. Furthermore, we found studies about the effects of 2,4-D in mixtures with other pesticides, as well as hepatoprotection trials. The reviewed data in-dicate that the reduction in antioxidant capacity and oxidative stress play an important role in 2,4-D-induced hepatotoxicity. However, the mechanism of action of the herbicide is still not ful-ly understood and further research in this area is needed.

We provide quantitative results from GIS-based modelling of urban emission functions for a range of representative low- and mid-rise locations, ranging from individual streets to residential communities within cities as well as entire towns and city regions with the aim of whether lantern photometry or built environment has the dominant effect on light pollution. We demonstrate the scalability of our work by providing results for the largest urban area modelled to date, comprising the central 117 km2 area of Dublin City and containing nearly 42,000 public lights. Our results show a general similarity in the shape of the azimuthally-averaged emission function for all areas examined, with differences in total light output distribution depending primarily on the nature of the lighting and, to a smaller extent, on the obscuring environment including seasonal foliage effects. A comparison with global satellite observations shows that they are consistent with the deduced angular emission function for other low-rise areas worldwide. We further validate our approach by comparing results for a range of urban locations by the close agreement observed in a detailed comparison of with calibrated imagery from the International Space Station. To our knowledge, this is the first such detailed quantitative verification of light loss calculations.

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.

The closed forms of the non-resonant thermonuclear function in the Maxwell-Boltzmann and Tsallis case with depleted tail are obtained in generalized special functions. The results are written in terms of H-function of two variables. The importance of the results in this paper lies in the fact that the reaction rate probability integrals in Maxwell-Boltzmann and Tsallis cases are not obtained by the conventional method of approximation or by means of a single variable transform technique but by means of a two variable transform method. The Behaviour of the depleted non-resonant thermonuclear functions are examined using graphs. The results in the paper are of much interest to astrophysicists and statisticians in their further work in this area.

Many cellular functions important for tumor initiation and progression are mediated by members of the integrin family, a diverse family of cell adhesion receptors. With recent studies emphasising on the role of the tumor microenvironment (TME) in tumor initiation and progression, it is not surprising that a lot of attention is being given to integrins. Several integrins are under trial with many demonstrating appealing activity in patients with different cancers. A deeper knowledge of the functions of integrins within the tumor microenvironment is still required, and might lead to better inhibitors being discovered. Integrin expression is commonly dysregulated in many tumors with integrins playing key roles in signaling as well as promotion of tumor cell invasion and migration. This review report new data on the differential expression of integrins within solid tumors using two publicly available resources: The Cancer Genomic Atlas (TCGA) and Gene Expression Profiling Interactive Analysis (GEPIA). In this analysis, I investigated the expression of integrin alpha 2 (ITGα2), ITGα3, ITGβ4 and ITGβ6 in tumor tissues versus adjacent normal tissues. This analysis showed that integrins were differentially expressed in cervical squamous cell carcinoma (CESC), head and neck squamous cell carcinoma (HNSC), esophageal carcinoma (ESCA) and lung adenocarcinoma (LUAD). This analysis showed that ITGα2 and ITGβ6 expression are upregulated in CESC and ESCA, ITGα3 is upregulated in HNSC and ESCA whilst ITGβ4 is highly expressed in CESC, HNSC, ESCA and LUAD tumor tissues compared to adjacent normal tissues. Integrins also play a major role in adhesion of circulating tumor cells to new sites and the resulting formation of secondary tumors. Furthermore, integrins have demonstrated the ability to promoting stem cell-like properties in tumor cells as well as drug resistance. Anti-integrin therapies rely heavily on the doses or concentrations used as these determine whether the drugs act as antagonists or as integrin agonists. This review offers the latest synthesis in terms of current knowledge of integrins functions within the tumor microenvironment and potential targets for different cancers.

We developed a novel hybrid approach for solving global optimization, computer science, bio-medical and engineering real life applications that is based on the coupling of the Whale Optimizer and Sine Cosine Algorithms via a surrogate model. We relate the whale optimizer algorithm to balance between the exploitation and the exploration process in the proposed method. There exist confirmed techniques for searching approximate best optimal solutions, but our algorithm will further guarantee that such numerical and statistical solutions satisfy physical bounds of the standard and real life functions. Our experiments with the benchmark, bio-medical, computer science and engineering real life problems have illustrated the advantages of using a newly hybrid approach based on mixing Whale Optimizer and Sine Cosine algorithms. It holds considerable potential for reducing execution time for solving standard and real life problems and at the same time improving the quality of the solution.

YH-DIE must have continuity . Given the basic algebraic clusters of homogeneous configurations,we can get the basic three equations: \begin{array}{l} {\mathop{\int}\nolimits_{0}\nolimits^{{x}_{i}}{\frac{{G}\left({{x}_{i}\mathrm{,}s}\right)}{{\left({{x}_{i}\mathrm{{-}}{s}}\right)}^{\mathit{\alpha}}}\mathrm{\varphi}\left({s}\right){ds}}\mathrm{{=}}{f}\left({{x}_{i}}\right)}\ ;\ {\frac{\mathrm{\partial}}{\mathrm{\partial}{x}_{i}}\left({\frac{{\mathrm{\partial}}_{{x}_{i}}G}{\sqrt{{1}\mathrm{{+}}{\left|{\mathrm{\nabla}{G}}\right|}^{2}}}}\right)\mathrm{{=}}{0}}\ ;\ {{i}\mathrm{{=}}\mathop{\sum}\limits_{{x}_{i}\mathrm{{=}}{1}}\limits^{\mathrm{\infty}}{\arccos\hspace{0.33em}\mathrm{\varphi}\left({{x}_{i}}\right)}\mathrm{{=}}{f}\left({\fbox{${Yuh}$}}\right)} \end{array} YH-DIE has become a fusion point and access point in the fields of algebraic geometry and partial differential equations, and its mapping on multidimensional algebraic clusters or manifolds is very special. The minimal surface equation is a special case.

In this paper, we study the convergence of new implicit iterations dealing with n-tupled fixed point results for nonlinear contractive-like mappings on W-hyperbolic metric spaces. Herein, we demonstrate that our newly implicit iteration schemes have faster rate of convergence than implicit S-iteration process, implicit Ishikawa and Mann type iteration processes. Furthermore, a numerical simulation to improve our theoretical results is obtained.

This paper presents the symmetries of differential equations associated with one-variable and Bivariate Hermite polynomials by proposing a representation of Lie algebra for these differential operators. Applying the Baker-Campbell-Hausdorff formula to these algebras, results in new relations and generating functions in one-variable and Bivariate Hermite polynomials. A general form of representation for other orthogonal polynomials such as Laguerre polynomials is introduced.

Pure silver as well as silver compounds have been used as antiseptics for centuries. Nowadays, the most frequently applied form of silver is a nanoparticle form. Several studies demonstrate the ability of silver nanoparticles and silver salts to accumulate in the brain of laboratory ani-mals as well as the ability of silver nanoparticles to influence behavioral and cognitive functions of laboratory mammals. For the first time, the influence of a silver salt, in particular, silver citrate on the change dynamics of behavioral and cognitive functions of laboratory mice at the daily oral exposure during 30, 60, 120 and 180 days is investigated in the present research. We observed the anxiety increase after 30 days of the exposure as well as the ability of mice to adapt to the prolonged oral exposure of silver citrate manifested in the anxiety decrease, increase of locomotor activity and the tendency of long-term contextual memory improvement. Increase of locomotor activity and memory improvement might be associated with the sensitivity increase and regarded as compensatory mechanism to anxiety increase. The observed phenomenon is classified as a hormetic effect. A comparison with the analogous study implemented polyvi-nylpyrrolidone coated silver nanoparticles is carried out. It was concluded that the nanoform is more neurotoxic.

New families of direct serendipity and direct mixed finite elements on general planar, strictly convex polygons were recently defined by the authors. The finite elements of index r are H1 and H(div) conforming, respectively, and approximate optimally to order r+1 while using the minimal number of degrees of freedom. The shape function space consists of the full set of polynomials defined directly on the element and augmented with a space of supplemental functions. The supplemental functions were constructed as rational functions, which can be difficult to integrate accurately using numerical quadrature rules when the index is high. This can result in a loss of accuracy in certain cases. In this work, we propose alternative ways to construct the supplemental functions on the element as continuous piecewise polynomials. One approach results in supplemental functions that are in Hp for any p≥1. We prove the optimal approximation property for these new finite elements. We also perform numerical tests on them, comparing results for the original supplemental functions and the various alternatives. The new piecewise polynomial supplements can be integrated accurately, and therefore show better robustness with respect to the underlying meshes used.