bluuebunny/crossref_metadata_2025 huggingface dataset:
Approximation by Generalized Faber Series in Weighted Bergman Spaces on Infinite Domains With a Quasiconformal Boundary
Authors: Israfilov Daniyal M. , Yildirir Yunus E.
Published: August 2024

Using an integral representation on infinite domains with a quasiconformal boundary the generalized Faber series for the functions in the weighted Bergman space $A^{2}(G,\omega )$ are defined and its approximation properties are investigated.
 
2000 Mathematics Subject Classification. 30E10, 41A10, 41A25, 41A58
Maximal Clifford Semigroups of Matrices
Authors: Lee Edmond W. H.
Published: August 2024

All maximal Clifford semigroups of matrices are identified up to isomorphism. If the ground field of the matrices is finite, then there exists a unique Clifford semigroup of maximum order.
 
2000 Mathematics Subject Classification. 20M25
On a New Inequality Similar to the Hardy - Hilbert Integral Inequality
Authors: Sulaiman W. T.
Published: August 2024

A new inequality similar to the Hardy-Hilbert integral inequality is proved. Some special cases are also deduced.
 
2000 Mathematics Subject Classification. 26D15
Measurability – Preserving Weakly Mixing Transformations
Authors: Fatkić Huse
Published: August 2024

In this paper we investigate measure-theoretic properties of the class of all weakly mixing transformations on a finite measure space which preserve measurability. The main result in this paper is the following theorem: If $\phi $ is a weakly mixing transformation on a finite measure space $( S, \mathcal A , \mu )$ with the property that $\phi (\mathcal A ) \subseteq \mathcal A ,$ then for every $A, B $ in $\mathcal A$ there is a subset $J(A,B)$ of the set of non-negative integers of density zero such that $\lim _{m \to \infty ,m \notin J(A,B)} \mu (A \cap \phi ^m(B)) = (\mu (A) / \mu (S))\lim _{n \to \infty } \mu \,(\phi^n(B)).$ Furthermore, we show that for most useful measure spaces we can strengthen the preceding statement to obtain a set of density zero that works for all pairs of measurable sets $A$ and $ B.$ As corollaries we obtain a number of inclusion theorems. The results presented here extend the well-known classical results (for invertible weakly mixing transformations), results of R. E. Rice [17] (for strongly mixing), a result of C. Sempi [19] (for weakly mixing) and previous results of the author [8, 10] (for weakly mixing and ergodicity).
 
2000 Mathematics Subject Classification. Primary: 28D05, 37A25; Secondary: 37A05, 47A35
On the Non-existence of Certain Types of Weakly Symmetric Manifold
Authors: Ghosh Amalendu
Published: August 2024

An expression for the curvature tensor of a weakly symmetric manifold is obtained. Next it is shown that an Einstein weakly symmetric manifold of dimension $>2$ does not exist. Further it is proved that a conformally flat weakly symmetric manifold of dimension $>3$ is a quasi Einstein manifold. Finally a couple of results on conformally flat weakly symmetric manifold are presented.
 
2000 Mathematics Subject Classification. 53B35, 53B05
Some Modifications of the Trapezoidal Rule
Authors: Udovičić Zlatko
Published: August 2024

By using the quadratic interpolating spline a new class of the quadrature rules was obtained. Those formulas are modifications of the well known trapezoidal rule. The basic characteristic of those formulas is a free parameter. With appropriate choice of that parameter, accuracy of the trapezoidal rule can be improved up to $O(h^4).$ Besides this, by using this nonstandard techniques some well known quadrature rules were also obtained.
 
2000 Mathematics Subject Classification. 65D32, 65D07
On Split Exact Sequences and Projective Semimodules
Authors: Bhambri S. K. , Dubey Manish Kant
Published: August 2024

In this paper the notion of split exact sequences of semimodules is introduced. We also study some results on projective semimodules that are analogous to module theory.
 
2000 Mathematics Subject Classification. 16Y60
A Common Fixed Point Theorem for Weakly Compatible Mappings in Compact Metric Spaces Satisfying an Implicit Relation
Authors: Aliouche Abdelkrim
Published: August 2024

We prove a common fixed point Theorem for four mappings in compact metric spaces satisfying an implicit relation using the concept of weak compatibility without decreasing assumption which generalizes Theorem 1 of V. Popa [9].
 
2000 Mathematics Subject Classification. 54H25, 47H10
Period-Two Trichotomies of a Difference Equation of Order Higher Than Two
Authors: Burgić Dževad , Kalabuˇsić S. , Kulenović M. R. S.
Published: August 2024

We investigate the period-two trichotomies of solutions of the equation $$x_{n+1} = f(x_{n}, x_{n-1},x_{n-2}), \quad n=0, 1, \ldots $$ where the function $f$ satisfies certain monotonicity conditions. We give fairly general conditions for period-two trichotomies to occur and illustrate the results with numerous examples.
 
1991 Mathematics Subject Classification. 39A10, 39A11
On the Composition of the Distributions ${x^{\lambda} _+ \ln^m x_+}$ and ${x_+^{-1/\lambda}}$
Authors: Fisher B. , Kraiweeradechachai T.
Published: August 2024

Let $F$ be a distribution and let $f$ be a locally summable...
 
2000 Mathematics Subject Classification. 46F10
Extremal Vectors for a Class of Operators
Authors: Downey Larry , Ong Boon W.
Published: August 2024

In this note, we study extremal vectors for a class of operators with a special application to the the Volterra operator. The study requires the description of the asymptotic behavior of a class of infinite series involving a real parameter.
 
2000 Mathematics Subject Classification. 47A05, 40C99
Existence of Weak Solutions for Nonlinear Systems Involving Degenerated p-Laplacian Operators
Authors: Serag H. M. , Khafagy S. A.
Published: August 2024

We study the existence of weak solutions for the nonlinear system\begin{equation*}\left.\begin{aligned}-\Delta _{P,_{p}}u&=a(x)|u|^{p-2}u-b(x)|u|^{\alpha }|v|^{\beta }v+f, \\-\Delta _{Q,q}v&=-c(x)|u|^{\alpha }|v|^{\beta }u+d(x)|v|^{q-2}v+g,\end{aligned}\right\}\end{equation*}where, the degenerated p-Laplacian is defined as $\Delta _{P,p}u=div [P(x)$ $|\nabla u|^{p-2}\nabla u].$ We prove the existence of weak solutions for this system defined on bounded domains using the theory of monotone operators. We also consider the case of an unbounded domain.
 
2000 Mathematics Subject Classification. 35J67, 35J55, 47H07
On a Discrete Hilbert Type Inequality With Non–Homogeneous Kernel
Authors: Draščić Ban Biserka , Pečarić Josip , Pogány Tibor K.
Published: August 2024

New extensions are given for the discrete Hilbert type inequality with non–homogeneous kernel. By this, recently published results by Pogány have been improved by a Hilbert type inequalities in homogeneous kernel case derived by Krnić and Pečarić. Mathematical tools also used are the Dirichlet series’ Laplace–integral representation and the classical Hölder inequality.
 
2000 Mathematics Subject Classification. Primary 26D15; Secondary 40B05, 40G99
On a Nonlinear Volterra Integral Equation in Two Variables
Authors: Pachpatte B. G
Published: August 2024

The aim of this paper is to study the existence, uniqueness and other properties of solutions of a certain nonlinear Volterra integral equation in two variables. The fundamental tools employed in the analysis are based on applications of the Banach fixed point theorem and a certain variant of the integral inequality with explicit estimate on the unknown function.
 
2000 Mathematics Subject Classification. 34K10, 35R10, 39A10
Two Results on the Commutative Product of Distributions and Functions
Authors: Fisher Brian
Published: August 2024

Let $f$ and $g$ be distributions and let $f_n=(f*\delta_n x)$ and $g_n =(g*\delta _n)(x)$, where $\delta _n(x)$ is a certain sequence converging to the Dirac delta-function. The product $f .g$ of $f$ and $g$ is defined to be the limit of the sequence $\{f_ng_n\}$, provided its limit $h$ exists in the sense that $$\lim _{n \to \infty} \langle f_n (x) g_n (x),\vphi (x) \rangle =\langle h(x), \vphi (x) \rangle $$ for all functions $\vphi$ in ${\mathcal D}.$ It is proved that \begin{align*}(\sgn x|x| ^{-r} \ln ^p |x|). ( |x| ^\mu \ln^q|x|)&=\sgn x |x| ^{-r +\mu } \ln ^{p+q}|x| ,\\(|x| ^{-r} \ln ^p |x|). (\sgn x |x| ^\mu \ln ^q|x| ) &=\sgn x |x| ^{-r +\mu } \ln ^{p+q}|x|\end{align*}for $-2<-r+\mu< -1,$ $r=1,2, \ldots$ and $p,q =0,1,2. \ldots .$
 
2000 Mathematics Subject Classification. 46F10
B.-Y. Chen Inequalities for Slant Submanifolds in Kenmotsu Space Forms II
Authors: Costache Simona
Published: August 2024

In this article, we investigate sharp inequalities involving Chen invariants for a slant submanifold $M$ of a Kenmotsu space form $\widetilde{M}(c)$, tangent to the structure vector field of the ambient space.
 
2000 Mathematics Subject Classification. 53C40, 53C25
Convolutions of Bernoulli and Euler Polynomials
Authors: Chu Wenchang , Zhou Roberta R.
Published: August 2024

By means of the generating function technique, several convolution identities are derived for the polynomials of Bernoulli and Euler.
 
2000 Mathematics Subject Classification. Primary 11B68, Secondary 05A15
On the Cohomology of Spaces of Links and Braids via Configuration Space Integrals
Authors: Volić Ismar
Published: August 2024

We study the cohomology of spaces of string links and braids in...
 
2000 Mathematics Subject Classification. Primary: 57M27; Secondary: 81Q30, 57R40
Curvature via the de Sitter’s Space-Time
Authors: Desideri Graciela María
Published: August 2024

We define the central curvature and the total central curvature of a closed curve in a Lorentz $(n + 1)$--space. In addition, we obtain estimates for the total central curvatures of spacelike pure polygons. The study is done by using the n-dimensional de Sitter's space-time.
 
2000 Mathematics Subject Classification. 53B30, 53C50
Sheaves of Paragraded Rings
Authors: Ilić-Georgijević Emil , Vuković Mirjana
Published: August 2024

In this paper we deal with sheaves of the category of paragraded rings with the same set of grades $\Delta,$ in short, the category of paragraded rings of type $\Delta,$ denoted by $R^P_\Delta.$ The definition of a sheaf of category $R^P_\Delta$ is the same as for any other category, but we are interested in the paragraded structure sheaf, as we named it here, and so, in some way we introduce the theory of paragraded structures into algebraic geometry. For this purpose we need to deal with homogeneous ideals, particularly, we need to introduce the prime spectrum of $R\in\mathrm{obj}(R^P_\Delta)$ and to analyze the localization of $R$.
 
2010 Mathematics Subject Classification. 16S60, 16S85, 16W99
Existence of Periodic Solutions for Totally Nonlinear Neutral Differential Equations With Variable Delay
Authors: Ardjouni Abdelouaheb , Djoudi Ahcéne
Published: August 2024

We use a modification of Krasnoselskii's fixed point theorem introduced by T. A. Burton (see $\left[ 1\right] $ Theorem $3$) to show that the totally nonlinear neutral differential equation with variable delay\begin{multline*}x^{\prime }(t)=-a(t)x^{3}(t)+c(t)x^{\prime }(t-g(t))Q^{\prime}\left( x\left( t-g(t)\right) \right)\\ +G\left(t,x^{3}(t),x^{3}(t-g(t))\right) ,\end{multline*}has a periodic solution. We invert this equation to construct a sum of a compact map and a large contraction which is suitable for applying the modification of Krasnoselskii's theorem. The results of $\left[ 5\right]$ are generalized. Finally, an example is given to illustrate our result.
 
2000 Mathematics Subject Classification. 34K20, 45J05, 45D05
On Generalized Lipschitzian Semitopological Semigroup of Self-Mappings With Applications
Authors: Imdad M. , Barakat Mohamed A. , Soliman Ahmed H.
Published: August 2024

In this paper, we use a generalized Lipschitzian type condition for a semigroup of self-mappings as employed in Imdad and Soliman (Fixed Point Theory Appl. Vol. (2010), Article ID 692401, 1-14) to prove a fixed point theorem for a generalized Lipschitzian left reversible semitopological semigroup of self-mappings defined on a p-uniformly convex Banach space, besides indicating some possible applications to our main result. Our results generalize and extend some results due to J. S. Jung and B. S. Thakur (Inter. Jour. Math. Math. Sci., 28 (1)(2001), 41-50).
 
2000 Mathematics Subject Classification. 47H10, 54H25
Paragraded Structures Inspired By Mathematical Logic
Authors: Džamonja Mirna
Published: August 2024

We use methods from mathematical logic to give new examples of paragraded structures, showing that at certain cardinals all first order structures are paragraded. We introduce the notion of biembeddability to measure when two paragraded structures are basically the same. We prove that the bi-embeddability of the paragraduating system gives rise to the bi-embeddability of the limiting structures. Under certain circumstances the converse is also true, as we show here. Finally, we show that one paragraded structure can have many graded substructures, to the extent that the number of the same is not always decidable by the axioms of set theory.
* This paper was presented at the International Scientific Conference Graded structures in algebra and their applications, dedicated to the memory of Prof. Marc Krasner, IUCDubrovnik, Croatia, September, 22-24, 2016.
Order, Type and Cotype of Growth for p-adic Entire Function
Authors: Escassut Alain , Boussaf Kamal , Boutabaa Abdelbaki
Published: August 2024

Let $\K$ be a complete ultrametric algebraically closed field and let ${\cal A}(\K)$ be the $\K$-algebra of entires functions on $\K$. For an $f\in {\cal A}(\K)$, similarly to complex analysis, one can define the order of growth as $\rho(f)=\dsp{\limsup_{r\to +\infty}{\log(\log(|f|(r))\over \log r}}$. When $\rho(f)\neq 0, +\infty$, one can define the type of growth as $\sigma(f)=\dsp{\limsup_{r\to +\infty}{\log(|f|(r))\over r^{\rho(f)}}}$. But here, we can also define the cotype of growth as $\psi(f)=\dsp{\limsup_{r\to +\infty}{q(f,r)\over r^{\rho(f)}}}$ where $q(f,r)$ is the number of zeros of $f$ in the disk of center $0$ and radius $r$. Then we have $\rho(f)\sigma(f)\leq \psi(f)\leq e\rho(f)\sigma(f)$. Moreover, if $\psi$ or $\sigma$ are veritable limits, then $\rho(f)\sigma(f)= \psi(f)$ and this relation is conjectured in the general case. Many other properties are examined concerning $\rho(f),\ \sigma(f),\ \psi(f)$. Particularly, we prove that if an entire function $f$ has finite order, then $\dsp{f'\over f^2}$ takes every value infinitely many times and applications are shown to branched values of meromorphic functions.
* This paper was presented at the International Scientific Conference Graded structures in algebra and their applications, dedicated to the memory of Prof. Marc Krasner, IUCDubrovnik, Croatia, September, 22-24, 2016.
$\mathcal{I}_{2}$-Asymptotically Lacunary Statistical Equivalence of Weight $g$ of Double Sequences of Sets
Authors: Kişi Ömer
Published: August 2024

In this paper, our aim is to introduce new notions, namely, Wijsman asymptotically $\mathcal{I}_{2}$-statistical equivalence of weight $g$, Wijsman strongly asymptotically $\mathcal{I}_{2}$-lacunary equivalence of weight $g$ and Wijsman asymptotically $\mathcal{I}_{2}$-lacunary statistical equivalence of weight $g$ of double set sequences. We mainly investigate their relationship and also make some observations about these classes.
Cesàro Means of Subsequences of Double Sequences
Authors: Taş Emre , Orhan Cihan
Published: August 2024

In this paper we characterize the convergence and $\left( C,1,1\right) $ summability of a double sequence. In particular we study conditions under which the convergence or $\left( C,1,1\right) $ summability of a double sequence carry over to that of its subsequences, \ and conversely, whether these properties for suitable subsequences imply them for the sequence itself. We show, for instance, that a bounded double sequence is $\left(C,1,1\right) $ summable if and only if almost all of its subsequences are $\left( C,1,1\right) $ summable.
Survey on the Kakutani problem in p-adic analysis I
Authors: Escassut Alain
Published: August 2024

Let $\K$ be a complete ultrametric algebraically closed field and let $A$ be the Banach $\K$-algebra of bounded analytic functions in the ''open'' unit disk $D$ of $\K$ provided with the Gauss norm. Let $Mult(A,\Vert \ . \ \Vert)$ be the set of continuous multiplicative semi-norms of $A$ provided with the topology of pointwise convergence, let $Mult_m(A,\Vert \ . \ \Vert)$ be the subset of the $\phi \in Mult(A,\Vert \ . \ \Vert)$ whose kernel is a maximal ideal and let $Mult_1(A,\Vert \ . \ \Vert)$ be the subset of the $\phi \in Mult(A,\Vert \ . \ \Vert)$ whose kernel is a maximal ideal of the form $(x-a)A$ with $ a\in D$. By analogy with the Archimedean context, one usually calls {\it ultrametric Corona problem, or ultrametric Kakutani problem} the question whether $Mult_1(A,\Vert \ . \ \Vert)$ is dense in $Mult_m(A,\Vert \ . \ \Vert)$. In order to recall the study of this problem that was made in several successive steps, here we first recall how to characterize the various continuous multiplicative semi-norms of $A$, with particularly the nice construction of certain multiplicative semi-norms of $A$ whose kernell is neither a null ideal nor a maximal ideal, due to J. Araujo. Here we prove that multbijectivity implies density. The problem of multbijectivity will be described in a further paper.
Some New Inequalities for the Strictly Monotonic Functions and Positive n-Tuples
Authors: Mesihović Behdžet A.
Published: August 2024

In this paper we give the generalization of the inequalities\begin{equation*}\begin{split}&n\sum^n_{i=1}a_i^{n} \geq \sum^n_{i=1}a_i^{t} \sum^n_{i=1}a_i^{n-t} \geq \sum^n_{i=1}a_i^{s} \sum^n_{i=1}a_i^{n-s} \geq (\sum^n_{i=1}a_i^\frac{n}{2})^{2} ,\\ & 0 < t < s < \frac{n}{2},\ a_i>0,\forall i \in \{{1,\dots,n}\},\end{split}\end{equation*}(see [3] and [1, p.~377], and the new results for the strictly monotonic functions and positive n-tuples.
Survey on the Kakutani problem in p-adic analysis II
Authors: Escassut Alain
Published: August 2024

Let $\K$ be a complete ultrametric algebraically closed field and let $A$ be the Banach $\K$-algebra of bounded analytic functions in the ''open'' unit disk $D$ of $\K$ provided with the Gauss norm. Let $Mult(A,\Vert \ . \\Vert)$ be the set of continuous multiplicative semi-norms of $A$ provided with the topology of pointwise convergence, let $Mult_m(A,\Vert \ . \ \Vert)$ be the subset of the $\phi \in Mult(A,\Vert \ . \ \Vert)$ whose kernel is a maximal ideal and let $Mult_1(A,\Vert \ . \ \Vert)$ be the subset of the $\phi \in Mult(A,\Vert \ . \ \Vert)$ whose kernel is a maximal ideal of the form $(x-a)A$ with $ a\in D$. By analogy with the Archimedean context, one usually calls ultrametric Corona problem, or ultrametric Kakutani problem the question whether $Mult_1(A,\Vert \ . \ \Vert)$ is dense in $Mult_m(A,\Vert \ . \ \Vert)$. In a previous paper, we have recalled the characterization of a large set of continuous multiplicative semi-norms and why the multbijectivity of the algebra $A$ would solve the Corona problem. Here we prove that multbijectivity in the general case. This implies that $Mult_1(A,\Vert \ . \ \Vert)$ is dense in $Mult_m(A,\Vert \ . \ \Vert)$, beginning by the case when $\K$ is spherically complete and generalizing next.
Projective Curves With Nice Normal Bundles and Containing a Prescribed Subset of a Hyperplane
Authors: Ballico Edoardo
Published: August 2024

Fix a hyperplane $H\subset \mathbb{P}^n$, $n>3$, and a finite set $S\subset H$. We give conditions on the integers $d$, $g$ and $\sharp (S)$ such that there exists a smooth and connected curve $X\subset \mathbb{P}^n$ with $\deg (X) =d$, $p_a(X)=g$ and $S\subset X\cap H$. When $d=\sharp (S)$ we may take $g$ up to order $2d/n$, $d\gg 0$, when $S$ is in linear general position. We also prove the existence of $X$ with $h^1(N_X(-1))=0$ if $n\ge 8$, $g$ is odd and $2d\ge (n-3)g+n+11$.
Weighted Hyers-Ulam Stability for Nonlinear Nonautonomous Difference Equations
Authors: Dragičević Davor
Published: August 2024

Let $(A_m)_{m\in \mathbb{Z}}$ be a sequence of bounded linear operators acting on an arbitrary Banach space $X$ and admitting an exponential dichotomy. Furthermore, let $f_m \colon X\to X$, $m\in \mathbb{Z}$ be a sequence of Lipschitz maps. Provided that the Lipschitz constants of $f_m$ are uniformly small, we show that a nonlinear difference equation $x_{m+1} = A_mx_m +f_m(x_m),   m\in \mathbb{Z}$ exhibits various types of the  Hyers-Ulam stability property.
The Periodic Integer Orbits of Polynomial Recursions With Integer Coefficients
Authors: Sedaghat Hassan
Published: August 2024

We show that polynomial recursions $x_{n+1}=x_{n}^{m}-k$ where $k,m$ are integers and $m$ is positive have no nontrivial periodic integer orbits for $m\geq3$. If $m=2$ then we show that the recursion has integer two-cycles for infinitely many values of $k$ but no higher period orbits. We further show that these statements are true for all quadratic recursions and comment on possible higher order extensions.
On the value sharing of $q$-$c$-shift and $q$-shift monomials of meromorphic functions and their derivatives
Authors: Banerjee Abhijit , Biswas Tania
Published: August 2024

In this paper, we employ the notion of weighted sharing to study the uniqueness problems of $q$-$c$-shift and $q$-shift monomials of transcendental meromorphic functions of zero order sharing $1$-points. The results in this paper extend some previous results.
A Study of a Non-local Initial Value Problem Fractionally Perturbed
Authors: Atmania Rahima
Published: August 2024

In this work, we study a class of fractionally nonlinearly perturbed ﬁrst order differential equations, subject to a nonlocal initial condition on an unbounded interval, which is the novelty here. By means of the principle of contraction mapping to establish the existence result and by a Gronwall-like inequality, we obtain the asymptotic stability and the λ-stability of the zero solution. Finally, we give an illustrative example.
Decomposable Extensions Between Rank 1 Modules in Grassmannian Cluster Categories
Authors: Bogdanic Dusko , Boroja Ivan-Vanja
Published: August 2024

Rank $1$ modules are the building blocks of the category ${\rm CM}(B_{k,n}) $ of Cohen-Macaulay modules over a quotient $B_{k,n}$ of a preprojective algebra of affine type $A$. Jensen, King and Su showed in \cite{JKS16} that the category ${\rm CM}(B_{k,n})$ provides an additive categorification of the cluster algebra structure on the coordinate ring $\mathbb C[{\rm Gr}(k, n)]$ of the Grassmannian variety of $k$-dimensional subspaces in $\mathbb C^n$. Rank $1$ modules are indecomposable, they are known to be in bijection with $k$-subsets of $\{1,2,\dots,n\}$, and their explicit construction has been given in [8]. In this paper, we give necessary and sufficient conditions for indecomposability of an arbitrary rank 2 module in ${\rm CM}(B_{k,n})$ whose filtration layers are tightly interlacing. We give an explicit construction of all rank 2 decomposable modules that appear as extensions between rank 1 modules corresponding to tightly interlacing $k$-subsets $I$ and $J$.
On a New Class Related to the Subclass of Close-To-Convex Functions
Authors: Singh Gagandeep , Singh Gurcharanjit
Published: August 2024

This paper is concerned with a generalized class of analytic functions which is related to the subclass of close-to-convex functions in the open unit disc $E=\{z:|z|<1\}$. The coefficient estimates, distortion theorem, growth theorem, argument theorem, radius of convexity, Fekete-Szegö inequality and inclusion relation for the functions belonging to this class have been established. The results so obtained will provide a new direction in the study of certain new subclasses of analytic functions.
Bernstein type $L_{p}$ inequalities for composition of polynomials
Authors: Malik Shabir Ahmad
Published: August 2024

Let $P(z)=a_{0}+\sum\limits_{v=\mu}^{n} a_v z^v\in\mathscr P_{n,~\mu}$ and $P(z)\neq 0$ for $|z|<k$, where $k\geq 1$, then for $0\leq p\leq\infty$, Gardner and Weems (J. Math. Anal. Appl. 219 (1998), 472-478) proved that\begin{align*}\|P'\|_{p}\leq\frac{n}{\|k^{\mu}+z\|_{p}}\|P\|_{p}.\end{align*}In this note, we consider a more general class of polynomials $P\circ Q\in\mathscr P_{mn,~\mu}$ defined by $(P\circ Q)(z)=P(Q(z))$, where $Q\in \mathscr P_m$ and provide an extension of the above inequality and related results.
Linear maps preserving the Cullis determinant of $(n+1)\times n$ matrices
Authors: Guterman Alexander , Yurkov Andrey
Published: August 2024

In this paper we give an explicit description of linear maps preserving the Cullis determinant of rectangular matrices of the size $(n+1)\times n.$ Unlike the result about the ordinary determinant, it appears that linear preservers of Cullis determinant can be singular. We provide the corresponding examples and characterize the case when these maps are non-singular.
Characterization of Weyl Functions in the Class of Operator-Valued Generalized Nevanlinna Functions
Authors: Borogovac Muhamed
Published: August 2024

We provide the necessary and sufficient conditions for a generalized Nevanlinna function $Q$ ($Q\in N_{\kappa }\left( \mathcal{H} \right)$) to be a Weyl function (also known as a Weyl-Titchmarch function).
We also investigate an important subclass of $N_{\kappa }(\mathcal{H})$, the functions that have a boundedly invertible derivative at infinity $Q'\left( \infty \right):=\lim \limits_{z \to \infty}{zQ(z)}$. These functions are regular and have the operator representation $Q\left( z \right)=\tilde{\Gamma}^{+}\left( A-z \right)^{-1}\tilde{\Gamma},z\in \rho \left( A \right)$, where $A$ is a bounded self-adjoint operator in a Pontryagin space $\mathcal{K}$. We prove that every such strict function $Q$ is a Weyl function associated with the symmetric operator $S:=A_{\vert (I-P)\mathcal{K}}$, where $P$ is the orthogonal projection, $P:=\tilde{\Gamma} \left( \tilde{\Gamma}^{+} \tilde{\Gamma} \right)^{-1} \tilde{\Gamma}^{+} $.
Additionally, we provide the relation matrices of the adjoint relation $S^{+}$ of $S$, and of $\hat{A}$, where $\hat{A}$ is the representing relation of $\hat{Q}:=-Q^{-1}$. We illustrate our results through examples, wherein we begin with a given function $Q\in N_{\kappa }\left( \mathcal{H} \right)$ and proceed to determine the closed symmetric linear relation $S$ and the boundary triple $\Pi$ so that $Q$ becomes the Weyl function associated with $\Pi$.
2020 Mathematics Subject Classification. 34B20, 47B50, 47A06, 47A56
The First Regularized Trace of the Sturm-Liouville Operator With Robin Boundary Conditions
Authors: Pavlović Komazec Nataša , Vojvodić Biljana
Published: August 2024

This paper deals with the boundary value problem for the operator Sturm-Liouville type $ D^{2}=D^{2}(h, H, q_{1},q_{2},\tau,\varphi)$ generated by$$-y''(x)+\sum_{i=1}^{2}q_i(x)y(x-i\tau)=\lambda y(x),\,x\in[0, \pi]$$$$y'(0)-hy(0)=0,\, y'(\pi)+Hy(\pi)=0$$where $\ds{\frac{\pi}{3}\leq \tau <\frac{\pi}{2}}$,\,\,$ h, H\in R\setminus\{0\}$ and $\lambda $ is a spectral parameter. We assume that $ q_i$, $i=1,2$ are real-valued potential functions from $ L_2 [0, \pi]$. We establish a formula for the first regularized trace of this operator.
2020 Mathematics Subject Classification. 34B09, 34B24, 34L10
Happy Birthday Alexei !
Authors: Vuković Mirjana
Published: August 2024

In addition, I would like to send my birthday greetings to Alexei Panchishkin my long-time friend from way back in 1975, when I first was on a study stay as a doctoral "stazhor" at the famous Moscow State University – Lomonosov and first met him. At that time Alexei was one of the best and brilliant students of one of the greatest and famous scientists Yuri Ivanovich Manin from the Moscow's Lomonosov University. It was during the golden age of Russian and Soviet Mathematics.
I met him, for the first time, at the Manin's lectures Algebraic Questions in Differential Equations, or, in other words, Theory of Korteweg – de Vries. Among the listeners, in the large Lomonosov's amphiteather 16-10, were numerous well-known leading Lomonosov's professors: A.I. Kostrikin, L.A. Skornykov, A.V. Mikhalev, E.S. Golod, V.A. Zorich, Yu.A. Bahturin, A.Yu. Olshansky, as well as domestic and foreign visiting professors, doctoral students, and students.
Alexei Panchihkin – Lomonosov’s professor became professor and professor emeritus of the Grenoble Alpes University and a well-known scientist in the amazing worlds of numbers, functions, and varieties – the field of algebraic number theory with a special reference to the arithmetic of automorphic forms and the theory of complex and $p$-adic zeta functions, as well as the founder of new mathematical directions:

Arithmetic of automorphic $p$-adic $L$-functions,
Algorithmic arithmetic of function fields,
Solution of a problem of Coleman-Mazur,

and the author of new mathematical notions named after him:

Panchishkin distributions and
Panchishkin condition for the existence of motivic $p$-adic $L$-functions.

Dear Alexei Panchshkin,
My sincere congratulations on your 70th anniversary, once more !
Best wishes of good health and many new achievements – new books and much enthusiasm in mathematics and life.
Mirjana Vuković
Legal Implications on the Status of Individual Companies of Shares Inheritable to Foreign Heirs
Authors: Safitri Nanda Melinia , Santoso Budi , Syafi'i R. Imam Rahmat
Published: August 2024

If a shareholder of an individual company who dies in a mixed marriage, then their shares will transfer to foreign entities. This situation can cause confusion regarding the company's status. Therefore, this research will examine and analyze the legal consequences that inheriting shares from foreign heirs can have on the company's status. This writing uses a type of normative juridical research supported by an argumentum per analogy approach. The results of the research show that the legal consequences of inheriting shares from foreign heirs is that the obligation to change the company’s status to a capital partnership company by changing the list of shareholders and adding capital to the company. If the heirs do not wish this change, they can transfer their shares either by gift, exchange, or selling. Can also make a deed of transfer of inheritance rights to the shares to one heir who is an Indonesian citizen.
Study on the Patterns of Inorganic Carbon Content in Two Land use Types in the Semi-Arid Region, Kadapa, Andhra Pradesh, India
Authors: Basha P. Osman , Reddy M. Sridhar
Published: August 2024

Soil inorganic carbon (SIC) and soil organic carbon (SOC) are the two important carbon reservoirs in the soils of semiarid regions. A total of 12 soil samples in each of the two study sites at two depths namely 0-10 cm and 10-30 cm were collected. SIC stock was variable and ranged from 0.8 to 2.23 % and maximum content was recorded in the subsurface layer in the Barren land. While higher SOC value was registered in the top surface layer in the cropland. Statistical ‘t’ test revealed significant difference in SIC distribution with depth as it increased with depth whereas SOC decreased with depth.
Response of Solanum lycopersicum L. Genotypes to Saline Stress on Seed Germination and Seedling Stage
Authors: Sivakumar J. , Basha P. Osman
Published: August 2024

Salt stress is one of the abiotic factors that restricted crop growth and productivity. One of the crucial approaches for addressing this issue is screening-based selection of germplasms that are resistant to salt stress. Seed germination and seedling development are the crucial stages of plant development that are most significantly affected by salt stress. The current study's objective is to compare the responses of 15 tomato genotypes to two different salt stress conditions. Experimental analysis of present research was carried in Agri-Science park laboratoty, Yogi Vemana University, YSR Kadapa at 2018. Tomato seeds were allowed to grow for ten days at control (non-saline), 75 mM and 125 mM salt stress conditions and analyzed the germination percentage, shoot lengths, root lengths, fresh weight, dry weight, and stress tolerance trait indices. All the studied variables have shown gradual decreases as a result of increased salt stress. The EC 251649, EC 251581, EC 164329, and EC 523851 genotypes has shown better germination than the other genotypes under tested stress conditions. The genotypes IC 164656 and EC 315478 have better fresh weight and dry weight under 125 mM salt stress, while the EC 177297 genotype has healthier root and shoot lengths among the studied germplasms. Our results revealed that a greater proportion of the variation in the parameters was accounted for type of germplasms. It can be inferred that seedling traits may serve as a valid criteria for choosing genotypes that are more tolerant of salinity stress at seedling stage.
Isolation and Characterisation of Octa Siloxane from Catharanthus roseus Leaf Extract by Molecular Docking Analysis as Insecticide Against, Aedes vittatus, (Diptera: Culicidae)
Authors: Anjaiah Chandra , Madhavi
Published: August 2024

Octa siloxane compound was isolated from Catharanthus roseus.and the sequences of three proteins (sterol Career protein, D7 protein and odorant - binding protein) were retrieved from Swissport database. the three-dimensional structure of these proteins was downloaded from PDB Database. The compound octa siloxane isolated and characterized from Catharanthus roseus, has been studied for use as a natural insecticide. The compound was previously evaluated for their bioactive and was found to possess potent larvicidal activity against the fourth instar larvae of Ae. vittatus. the inhibitor octa siloxane with pronounced larvicidal activity was subjected to computational screening and was used as a tool to study the mode of action and molecular mechanism of the selected functional protein. The ligand (compound) structure was drawn using ACD Che Sketch and converted in to PDB format using Open Babel. The 3D structures of proteins were docked with the inhibitor octa siloxane using Patch dock tool. The 2D and 3D chemical structure of the ligand/compound isolated from Catharanthus roseus, was retrieved from PubChem data base.
Green Synthesis and Characterization of Zinc Oxide Nanoparticles from Mukia maderaspatana (L.) Roem. Leaf Extract and their Antibacterial Activity
Authors: V. Catherine Sheeja , A. Anami Augustus Arul , S. Ani Besant , R. Blessy , Alexander Hanna Jeeja
Published: August 2024

Objective: To green synthesize and characterize zinc oxide nanoparticles from Mukia maderaspatana (L.) Roem. Leaf extract and study its antibacterial activity.
Materials and Methods: The leaves of Mukia maderaspatana were collected, shade dried, powdered and leaf extract was prepared using standard procedure. Zinc oxide nanoparticles was synthesized using the leaf extract, followed by characterization studies such as UV-Vis, FT-IR and SEM were carried out. The synthesized zinc oxide nanoparticles was used for anti-microbial activity.
Results and Discussion: Morphological, structural and antimicrobial properties of synthesized nanoparticles are characterized by using UV-Vis Spectrophotometer, FT-IR and SEM followed by Antimicrobial study using Disc Diffusion Method. The UV Vis spectroscopic analysis of synthesized zinc nanoparticles showed the maximum absorbance at 265.50 nm. SEM analysis shows that synthesized nanoparticles are found to be predominantly hexagonal in shape. Zinc oxide nanoparticles inhibited Escherichia coli with an inhibition zone of 16 mm.
Conclusion: The study reveals an efficient, ecofriendly and simple method of green synthesis of ZnO nanoparticles using green synthetic approach.
Effect of Different Feeder Designs on the Development of Osmanabadi Goat Kids
Authors: Kankarwal Gaurav , Pathak Rupal , Bhagat Vandana , Singh Nishma , Doneria Raina , Parmar Mehtab S. , Kanwar Kanti
Published: August 2024

The effect of feeder design on the growth performance of the Osmanabadi goat kids was investigated at the Seed Centre for Osmanabadi Goats-DRS Farm, Dau Shri Vasudev Chandrakar Kamdhenu Vishwavidyalaya, Durg, (CG, India) for a period of 60 days during the winter season. A total of 18 Osmanabadi weaned kids were randomly divided into three groups with six kids (3 males and 3 females) in each group viz T1, T2 and T3. T1 group kids (control) were kept on conventional feeder, T2 on circular feeder and T3 on linear feeder. The maximum (P>0.05) mean body weight was observed on the 60th day in T3 (13.23±0.33), as compared to T2 followed by T1. Similarly, a significantly higher mean body length was observed in T3 as compared to T1 and T2 groups on 45th and 60th day of the study. The maximum mean heart girth was observed on the 60th day in T3 (57.5±0.67) followed by T2 (55.3±1.4). Furthermore, the maximum mean height at wither was observed on the 60th day in T3 (58.1 ± 0.7) than T2 (57.1 ± 0.7) and T1 (55.8 ± 1.7). Our results revealed that modified linear feeder design positively influenced the growth performance of goat kids.
The Role of Bee Products in Cosmetic and Skincare Industry: Current Trends and Future Prospects
Authors: Gupta Garima , Rawat Divyanshi , Aggarwal Rahul
Published: August 2024

In recent years, honey-based products have gotten a lot of attention for the interesting and varied ways they can be used in cosmetics and skin care. Venom, royal jelly, honey, beeswax, and propolis are among the most well-known bee products. For the goal of healing and maintaining skin health, each part has its own special properties. This review article will examine the potential uses of bee products in the beauty and skincare industries. The purpose of this study is to synthesize previous research with current advancements in order to provide a thorough review of bee-derived compounds and their potential to transform the cosmetics industry. Each bee product is investigated for its distinct cosmetic uses, revealing information on how it moisturizes, rejuvenates, and protects the skin. It is the goal of this study to give a deep look into the latest market trends in honey-based skin care goods. As the need for options that are better for the environment and your skin grows, bee products have become a good choice. Knowing what chemicals are in them and how they can help with cosmetics gives both customers and professionals in the field useful information to help them make smart decisions. This review also shows the current trends in the skin care market, which helps us understand the future of bee products in the beauty business. Consumers are looking for eco-friendly and effective ways to take care of their skin, so honey-based cosmetics are likely to become more popular.
Unveiling the Ancient Wisdom: Antibacterial and Antifungal Properties of Pavetta indica
Authors: Baskaran Thanaraj , Koperuncholan Marimuthu
Published: August 2024

This study investigated the antibacterial and antifungal properties of Pavetta indica leaves using an ethanolic extract (PI). The agar well diffusion method revealed dose-dependent inhibition zones against various bacterial and fungal strains. Notably, the extract demonstrated promising antifungal activity against Cryptococcus neoformans, comparable to the positive control (Amphotericin B) for fungal activity. All tested bacterial strains (E. coli, Streptococcus faecalis, Bacillus subtilis, Pseudomonas aeruginosa) and fungal strains (Candida albicans, Aspergillus fumigatus, Sporothrix schenckii) exhibited susceptibility to PI, with inhibition zones increasing proportionally with extract concentration. Overall, this study suggests that P. indica leaves possess promising potential as a natural source of broad-spectrum antimicrobial and antifungal agents.
Die Teilkündigung gemäß § 648a Abs. 2 BGB im Lichte neuerer Rechtsdogmatik
Authors: Richter-Göbel Isabell
Published: August 2024

As part of the 2018 reform of construction contract law, the option of partial termination was implemented by law in Section 648a (2) BGB in addition to termination for good cause of the entire contract. This work examines the opportunities and risks in the application of partial termination. In addition to the dogmatic classification of the legal institution, it analyzes the requirements and legal consequences of the provision of section 648a (2) BGB and its problem areas. Following on from this, the transferability of this possibility to other termination rights such as the free partial termination pursuant to Section 648 BGB is examined. In addition, the consequences of an ineffective partial termination pursuant to Section 648a (2) BGB are discussed in order to counter these risks when drafting contracts.
Rechtsphilosophie und Rechtstheorie
Authors: Mahlmann Matthias
Published: August 2024

Das moderne Recht wirft viele grundsätzliche Fragen auf: Ist Recht mit Gerechtigkeit notwendig verbunden? Was ist überhaupt Recht und was Gerechtigkeit? Wie verhalten sich Recht und Moral zueinander? Warum und unter welchen Bedingungen ist Recht verbindlich? Diesen und zahlreichen anderen Fragen zu Recht, Ethik und ihrer Bedeutung für Staat und Gesellschaft geht Mahlmann in seinem Lehrbuch anhand von vielen Beispielen nach – von der Folter über die neuen Herausforderungen künstlicher Intelligenz für das Recht bis hin zu Perspektiven einer internationalen Friedensordnung in einer Epoche neuer Kriege. Dabei schlägt er einen Bogen von der Antike bis in die Gegenwart und entwickelt vor diesem historischen Hintergrund Antworten auf zentrale systematische Fragen der Rechtsphilosophie und Rechtstheorie.
Diktatur und Gewissen
Authors: Obenauer Julian
Published: August 2024

The book offers insights into the motives of perpetrators and victims of political repression in the SED regime. Biographical interviews from the archives of the Hohenschönhausen Memorial are used to analyse these motives using the method of analytical hermeneutics. The narrative analysis of these interviews remains a desideratum. The philosophical definition of central concepts such as motives and conscience as well as the history of ideas of the communist concept of order and morality form the basis of the empirical investigation. The analysis of the interviews documents the peculiar relationship between communist dictatorship and individual conscience.
Geschlechtsidentität und Recht
Authors: Grohs Kristina Maximiliane
Published: August 2024

The question of which benefit claims non-binary persons may have against the SHI in connection with gender affirming surgery in accordance with Section 27 (1) sentence 1 SGB V has not yet been uniformly clarified by the social courts. This topic is also quite new in the medical and legal literature. This work therefore begins by reviewing the current state of medical knowledge and findings. It then summarizes the current case law of the social courts, which is critically classified taking into account the relevant literature. Based on this, the author develops possible criteria according to which corresponding claims of non-binary insured persons could be assessed in the future. In the course of her doctorate, the author specialized in the field of medical law, in which she now works as a lawyer.
Fiber Bragg Grating Sensors Subjected to Mechanical and Hygrothermal Load
Authors: Aceti Pietro ,   Politecnico di Milano, Bettini Paolo , Sala Giuseppe ,   Politecnico di Milano,   Politecnico di Milano
Published: August 2024

In recent decades, the aviation industry has embraced the use of composite

materials in various aircraft components. However, these materials face challenges in

extreme environmental conditions during the operational life of aircraft. One

prominent issue contributing to safety concerns is the potential failure of composite

components due to the degradation of their mechanical properties caused by moisture

absorption. Numerous aviation accidents have been linked to this phenomenon,

underscoring the critical need for robust monitoring systems to ensure the continued

performance and structural integrity of composite structures.

To address this challenge, this research analyzes the effect of hygrothermal load on

Fiber Bragg Grating (FBG) sensors. We present a new mathematical formulation that

takes into account the contributions of mechanical strain, thermal expansion, and

hygroscopic swelling to the normalized Bragg wavelength variation. This

formulation, developed by differentiating the Bragg equation and applying

compatibility equations through the rules of mixtures, allows for accurate

measurement by accounting for humidity-induced deformations and avoiding

measurement errors related to moisture absorption.
Sunni-Shia Views of the Status of ‘Adalah's Companions of the Prophet
Authors: Mahasin Haikal Amanullah  , Muhammad Adip Fanani
Published: August 2024

Hadith science is a science that is closely related to history. A hadith can be said to be authentic if it has the quality of continuous sanad and fair narrators. The problem is, in moving towards justice, there are striking differences between Sunnis and Shiites. Sunnis are of the view that all the companions of the Prophet must be 'just. So there is no need to doubt the hadith narrated by them. On the other hand, the Shiites consider that they all apostated after the death of the Prophet Muhammad and they died as infidels. As a result of this disbelief, the friends are automatically eliminated from being fair. Because the first condition for justice is Islam. Each of these two groups quoted many verses from the Koran and hadith to strengthen their arguments. This article will explain the polemic of the debate on the nature of justice between Sunnis and Shiites. Firstly by explaining the meaning of Companions, the views of the two groups, and finally criticizing the opinions and arguments used by the two groups above. This research uses the library research method by examining the opinions expressed by the ulama, including the interpretation of verses, hadith sharah, and the ijtihad of the fuqoha'.
Φύσιs in Plato’s Republic
Authors: McDavid Brennan ,   Philosophy Documentation Center
Published: August 2024

I examine the role of nature (φύσιs) in the argument of Plato’s Republic and demonstrate that the concept plays a more central role in advancing the dialogue’s philosophical aims than has been appreciated by scholars. Socrates carefully distinguishes between the nature with which one is born and the nature that one has at the end of education. The former is one’s “original nature,” and the latter is that same original nature brought to fulfillment, a “fulfilled nature”. Both of these are referred to as φύσιs. Distinguishing them aids us in understanding the argument of the dialogue.
Seneca on Moral Improvement through Dialectical Study
Authors: Shogry Simon ,   Philosophy Documentation Center
Published: August 2024

Does Seneca entirely reject the utility of dialectical study for moral improvement? No, I argue here. Focusing on Letter 87, I propose that Seneca raises and disarms objections to formal Stoic arguments to help moral progressors avoid backsliding and advance towards ethical knowledge. I trace this method back to Chrysippus and show that reading Letter 87 in this Chrysippean framework yields a satisfying explanation of its otherwise puzzling features.
Pengaruh Psychological Safety terhadap Kinerja Karyawan Hotel Bintang 3 dan 4 di Kota Padang
Authors: Edfi Amelia Rahma , Rinaldi Rinaldi
Published: August 2024

This study was conducted with the aim of examining the impact of psychological safety on the performance of employees of 3 and 4 star hotels in Padang City. The research method is quantitative with purposive sampling. The sample consisted of 103 employees of 3 and 4 star hotels in Padang City. Data collection using psychological safety and employee performance scales (Individual Work Performance Questionnaire). The results showed a positive influence between psychological safety and employee performance of 77% (R = 0.277, R Square = 0.077, p<0.05). The level of psychological safety and employee performance on the subject is in the category of very low tendency. The results of this study found that the lower the psychological safety that employees experience, the lower will the resulting performance. The findings confirm the importance of improving employee psychological safety in order to improve performance.