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A new Bayesian–inspired statistic for hypothesis testing is proposed which compares two posterior distributions; the observed posterior and the expected posterior under the null model. The Kullback–Leibler divergence between the two posterior distributions yields a test statistic which can be interpreted as a penalized log–Bayes factor with the penalty term converging to a constant as the sample size increases. Hence, asymptotically, the statistic behaves as a Bayes factor. Viewed as a penalized Bayes factor, this approach solves the long standing issue of using improper priors with the Bayes factor, since only posterior summaries are needed for the new statistic. Further motivation for the new statistic is a minimal move from the Bayes factor which requires no tuning nor splitting of data into training and inference, and can use improper priors. Critical regions for the test can be assessed using frequentist notions of Type I error.

Efficient computational algorithms for bootstrapping linear regression models with clustered data are discussed. For ordinary least squares (OLS) regression, a new algorithm is provided for the pairs cluster bootstrap, along with two algorithms for the wild cluster bootstrap. One of these is a new way to express an existing method. For instrumental variables (IV) regression, an efficient algorithm is provided for the wild restricted efficient cluster (WREC) bootstrap. All computations are based on matrices and vectors that contain sums of squares and cross-products for the observations within each cluster, which have to be computed just once before the bootstrap loop begins. Monte Carlo experiments are used to study the finite-sample properties of bootstrap Wald tests for OLS regression and of WREC bootstrap tests for IV regression.

Distributional regression models that overcome the traditional focus on relating the conditional mean of the response to explanatory variables and instead target either the complete conditional response distribution or more general features thereof have seen increasing interest in the past decade. The current state of distributional regression will be discussed, with a particular focus on the four most prominent model classes: (i) generalized additive models for location, scale and shape, (ii) conditional transformation models and distribution regression, (iii) density regression, and (iv) quantile and expectile regression. Characteristics of the different distributional regression approaches will be provided to establish a structured overview on the similarities and differences with respect to the required assumptions on the conditional response distribution, theoretical properties, and the availability of software implementations. In addition, challenges arising in the interpretability of distributional regression models will be discussed and all four approaches will be illustrated with an application analyzing determinants of income distributions from the German Socio-Economic Panel (GSOEP).

Score-driven models provide a solution to the problem of modeling time series when the observations are subject to censoring and location and/or scale may change over time. The method applies to generalized t and EGB2 distributions, as well as to the normal distribution. Explanatory variables can be included, making static Tobit models a special case. A set of Monte Carlo experiments show that the score-driven model provides good forecasts even when the true model is parameter-driven. The viability of the new models is illustrated by fitting them to data on Chinese stock returns.

In this paper, we establish an Orlicz dual of the log-Aleksandrov–Fenchel inequality, by introducing two new concepts of dual mixed volume measures, and using the newly established Orlicz dual Aleksandrov–Fenchel inequality. The Orlicz dual log-Aleksandrov– Fenchel inequality in special cases yields the classical dual Aleksandrov–Fenchel inequality and some dual logarithmic Minkowski type inequalities, respectively. Moreover, the dual log-Aleksandrov–Fenchel inequality is therefore also derived.

Given partially ordered sets (posets) $(P, \leq_P)$ and $(P', \leq_{P'})$, we say that $P'$ contains a copy of $P$ if for some injective function $f: P\rightarrow P'$ and for any $X, Y\in P$, $X\leq _P Y$ if and only of $f(X)\leq_{P'} f(Y)$. For any posets $P$ and $Q$, the poset Ramsey number $R(P,Q)$ is the least positive integer $N$ such that no matter how the elements of an $N$-dimensional Boolean lattice are colored in blue and red, there is either a copy of $P$ with all blue elements or a copy of $Q$ with all red elements. We focus on a poset Ramsey number $R(P, Q_n)$ for a fixed poset $P$ and an $n$-dimensional Boolean lattice $Q_n$, as $n$ grows large. We show a sharp jump in behaviour of this number as a function of $n$ depending on whether or not $P$ contains a copy of either a poset $V$, i.e. a poset on elements $A, B, C$ such that $B>C$, $A>C$, and $A$ and $B$ incomparable, or a poset $\Lambda$, its symmetric counterpart. Specifically, we prove that if $P$ contains a copy of $V$ or $\Lambda$ then $R(P, Q_n) \geq n +\frac{1}{15} \frac{n}{\log n}$. Otherwise $R(P, Q_n) \leq n + c(P)$ for a constant $c(P)$. This gives the first non-marginal improvement of a lower bound on poset Ramsey numbers and as a consequence gives $R(Q_2, Q_n) = n + \Theta (\frac{n}{\log n})$., Comment: 18 pages, 2 figures

In this paper, a local minimum result for differentiable functionals is exploited in order to prove that a perturbed Dirichlet boundary value problem including a Lipschitz continuous non-linear term admits at least one non-trivial weak solution under an asymptotical behaviour of the nonlinear datum at zero. Some special cases and a concrete example of an application is then presented.

Derived actions in the category of groups with action on itself $\mathbf{Gr}^{\bullet}$ are defined and described. This category plays a crucial role in the solution of Loday's two problems stated in the literature. A full subcategory of reduced groups with action $\mathbf{rGr}^{\bullet}$ of $\mathbf{Gr}^{\bullet}$ is introduced, which is not a category of interest but has some properties, which can be applied in the investigation of action representability in this category; these properties are similar to those, which were used in the construction of universal strict general actors in the category of interest. Semi-direct product constructions are given in $\mathbf{Gr}^{\bullet}$ and $\mathbf{rGr}^{\bullet}$ and it is proved that an action is a derived action in $\mathbf{Gr}^{\bullet}$ (resp. $\mathbf{rGr}^{\bullet}$) if and only if the corresponding semi-direct product is and object of $\mathbf{Gr}^{\bullet}$ (resp. $\mathbf{rGr}^{\bullet}$). The results obtained in this paper will be applied in the forthcoming paper on the representability of actions in the category $\mathbf{rGr}^{\bullet}$., Comment: 12 pages, research paper, LaTeX2e, xypic

In this paper, warped product CRCR-submanifolds in Kahler manifolds and warped product contact CRCR-submanifolds in Sasakian, Kenmotsu and cosymplectic manifolds, are shown to possess a geometric property; namely DTDT-minimal. Taking benefit from this property, an optimal general inequality is established by means of the Gauss equation, we leave cosyplectic because it is an easy structure. Moreover, a rich geometry appears when the necessity and sufficiency are proved and discussed in the equality case. Applying this general inequality, the inequalities obtained by Munteanu are derived as particular cases. Up to now, the method used by Chen and Munteanu can not extended for general ambient manifolds, this is because many limitations in using Codazzi equation. Hence, Our method depends on the Gauss equation. The inequality is constructed to involve an intrinsic invariant (scalar curvature) controlled by an extrinsic one (the second fundamental form), which provides an answer for the well-know Chen's research problem (Problem 1.1???). As further research directions, we have addressed a couple of open problems arose naturally during this work and depending on its results.

Using the estimations of the even-indexed Bernoulli number and Euler number this paper established some new inequalities for the three functions $2\left( \sin x\right) /x+\left( \tan x\right) /x$, $\left( \sin x\right) /x+2\left( \tan (x/2)\right) /\left( x/2\right) $ and $2x/\sin x+x/\tan x$ bounded by the powers of tangent function.

Aims Multinomial logistic regression models allow one to predict the risk of a categorical outcome with > 2 categories. When developing such a model, researchers should ensure the number of participants ([Formula: see text]) is appropriate relative to the number of events ([Formula: see text]) and the number of predictor parameters ([Formula: see text]) for each category k. We propose three criteria to determine the minimum n required in light of existing criteria developed for binary outcomes. Proposed criteria The first criterion aims to minimise the model overfitting. The second aims to minimise the difference between the observed and adjusted [Formula: see text] Nagelkerke. The third criterion aims to ensure the overall risk is estimated precisely. For criterion (i), we show the sample size must be based on the anticipated Cox-snell [Formula: see text] of distinct ‘one-to-one’ logistic regression models corresponding to the sub-models of the multinomial logistic regression, rather than on the overall Cox-snell [Formula: see text] of the multinomial logistic regression. Evaluation of criteria We tested the performance of the proposed criteria (i) through a simulation study and found that it resulted in the desired level of overfitting. Criterion (ii) and (iii) were natural extensions from previously proposed criteria for binary outcomes and did not require evaluation through simulation. Summary We illustrated how to implement the sample size criteria through a worked example considering the development of a multinomial risk prediction model for tumour type when presented with an ovarian mass. Code is provided for the simulation and worked example. We will embed our proposed criteria within the pmsampsize R library and Stata modules.

A new family of multivariate copulas constructed from existing copulas by transforming the corresponding random variables using their conditional distributions are introduced. It is shown that for symmetrical copulas in a triangular scheme, this transformation tends to asymptotic independence.

There is a growing demand for the development of new statistical models and the refinement of established methods to accommodate different data structures. This need arises from the recognition that traditional statistics often assume the value of each observation to be precise, which may not hold true in many real-world scenarios. Factors such as the collection process and technological advancements can introduce imprecision and uncertainty into the data. For example, consider data collected over a long period of time, where newer measurement tools may offer greater accuracy and provide more information than previous methods. In such cases, it becomes crucial to restructure the data to account for imprecision and incorporate uncertainty into the analysis. Furthermore, the increasing availability of large datasets has introduced computational challenges in analyzing and processing the data. Representing the data in terms of intervals can help address this uncertainty by reducing the data size or accommodating imprecision. Traditional methods have already embraced this concept, but given the rising popularity of machine learning, it is essential to develop models for interval-valued data within the machine learning framework. Tree-based methods, in particular, are well-suited for handling interval-valued data due to their robustness to outliers and their nonparametric nature. Therefore, we propose a new model that takes into account the natural structure of the interval-valued data.. These tree-based methods offer improvements over existing models for interval-valued data, providing a framework capable of effectively handling data with uncertainty arising from imprecision or the need for size management.

Many discipline specific researchers need a way to quickly compare the accuracy of their predictive models to other alternatives. However, many of these researchers are not experienced with multiple programming languages. Python has recently been the leader in machine learning functionality, which includes the PyCaret library that allows users to develop high-performing machine learning models with only a few lines of code. The goal of the stressor package is to help users of the R programming language access the advantages of PyCaret without having to learn Python. This allows the user to leverage R’s powerful data analysis workflows, while simultaneously leveraging Python’s powerful machine learning functionality. stressor also implements a series of synthetic data set generation functions that create data sets where users can test ideas with models they create and/or use. These data sets can be paired with various forms of accuracy comparison to stress-test the models predictive capacity. This thesis illustrates this stress-test workflow on both real and synthetic data, illustrating stressor’s utility and ease of use.

For each of (i) arbitrary stochastic reset, (ii) deterministic reset with arbitrary period, (iii) reset at arbitrary constant rate, and then in the sense of either (a) first-order stochastic dominance or (b) expectation (i.e. for each of the six possible combinations of the preceding), those laws of random times are precisely characterized that are rendered no bigger [rendered no smaller; left invariant] by all possible restart laws (within the classes (i), (ii), (iii), as the case may be). Partial results in the same vein for reset with branching are obtained. In particular it is found that deterministic and arbitrary stochastic restart lead to the same characterizations, but this equivalence fails to persist for exponential (constant-rate) reset.

The literature on latent change score models does not discuss the importance of using a precise time metric when structuring the data. This study examined the influence of time metric precision on model estimation, model interpretation, and parameter estimate accuracy in bivariate LCS (BLCS) models through simulation. Longitudinal data were generated with a panel study where assessments took place during a given time window with variation in start time and measurement lag. The data were analyzed using precise time metric, where variation in time was accounted for, and then analyzed using coarse time metric indicating only that the assessment took place during the time window. Results indicated that models estimated using the coarse time metric resulted in biased parameter estimates as well as larger standard errors and larger variances and covariances for intercept and slope. In particular, the coupling parameter estimates – which are unique to BLCS models – were biased with larger standard errors. An illustrative example of longitudinal bivariate relations between math and reading achievement in a nationally representative survey of children is then used to demonstrate how results and conclusions differ when using time metrics of varying precision. Implications and future directions are discussed.

In this paper, we consider the Le Roy-type Mittag-Leffler function. Our main focus is to establish some sufficient conditions so that the normalized Le-Roy type Mittag-Leffler function posses some geometric properties such as starlikeness, convexity, close-to-convexity (univalency) and uniformly convexity inside the unit disk. Using these results, geometric properties of the normalized Mittag-Leffler function are derived as application. Results obtained in this paper are new. Interesting consequences, corollaries and examples are provided to support that these results are better and improve several results available in the literature.

This paper deals with some universal spaces. For every topological space $X$, the universal $T_1$ space is viewed as the bottom element of the lattice $\mathcal{L}_X$. The class of morphisms in $\mathrm{\mathbf{Top}}$ orthogonal to all $T_1$ spaces is characterized. Also, we introduce some new separation axioms and characterize them. Moreover, we characterize topological spaces $X$ for which the universal $T_1$ space associated with $X$ is a spectral space. Finally, we give some characterizations of topological spaces such that their $T_1$-reflection are compact spaces.

Over the years, different types of hyperideals have been introduced in order to let us fully realize the structures of hyperrings in general. ‎ ‎The aim of this research work is to define and characterize a new class of hyperideals in a Krasner ‎$‎(m,n)‎$‎-hyperring that we call ‎n-ary ‎‎$‎J‎$‎-hyperideals. A proper hyperideal ‎$‎Q‎$ o‎f a ‎Krasner ‎$‎(m,n)‎$‎-hyperring with the scalar identity ‎$‎1_R‎$ ‎is said to be an n-ary ‎$J‎$‎-hyperideal ‎‎‎‎if whenever $x_1^n \in R$ such that ‎$‎g(x_1^n) ‎\in ‎Q‎$ ‎and ‎‎$‎x_i \notin J_{(m,n)}(R)$, then ‎$‎g(x_1^{i-1},1_R,x_{i+1}^n) \in Q‎$‎. Also, we study the concept of n-ary ‎$‎\delta‎$‎-‎$‎J‎$‎-hyperideals as an expansion of n-ary $‎J‎$‎-hyperideals. Finally, we extend the notion of n-ary $‎\delta‎$‎-‎$‎J‎$‎-hyperideals to ‎$‎(k,n)‎$‎-absorbing ‎$‎\delta‎$‎-‎$‎J‎$-hyperideals.‎ ‎Let $\delta$ be a hyperideal expansion of a Krasner $(m,n)$-hyperring $R$ and $k$ be a positive integer‎. ‎A proper hyperideal $Q$ of $R$ is called $(k,n)$-absorbing $\delta‎$‎-‎$‎J‎$‎-hyperideal if for $x_1^{kn-k+1} \in R$‎, ‎$g(x_1^{kn-k+1}) \in Q$ implies that $g(x_1^{(k-1)n-k+2}) \in J_{(m,n)}(R)$ or a $g$-product of $(k-1)n-k+2$ of $x_i^,$ s except $g(x_1^{(k-1)n-k+2})$ is in $\delta(Q)$‎.

For a finite positive Borel measure μ on the unit circle, let D(μ) be the associated harmonically weighted Dirichlet space. A shift invariant subspace M recognizes strong approximate spectral cosynthesis if there exists a sequence of shift invariant subspaces M_k, with finite codimension, such that the orthogonal projections onto M_k converge in the strong operator topology to the orthogonal projection onto M. If μ is a finite sum of atoms, then we show that shift invariant subspaces of D(μ) admits strong approximate spectral cosynthesis.

A new transformation from terminating balanced $_4F_3$-series to $_3F_2$-series is proved that contains a few known summation formulae as special cases. Further closed form evaluations are given for terminating well--poised $_7F_6$-series as applications.

The aim of this paper is to introduce semitopological $\delta$-group and topological $\delta$-group with the concept of $\delta$-group which arise from approximately algebraic structures. Furthermore, it is shown that product space determined with $\delta$-topological subspaces is a $\delta$-topological space. Fundamental system of open $\delta$-neighborhoods and related properties were investigated.

In this study, we introduce a new class of the hyperbolic matrix functions which are called symmetrical hyperbolic Horadam sine and cosine matrix functions and we present some hyperbolic and recursive properties of these new matrix functions. In addition, we introduce quasi-sine Horadam matrix function and also define the matrix form of the metallic shofars that related to the hyperbolic Horadam sine and hyperbolic Horadam cosine matrix functions.

Let G be a finite group and S be a proper subgroup of G. A group G is called an S-(CAP)-group if every local subgroup of G is either a CAP-subgroup or conjugate to a subgroup of S. The main purpose of this construction is to demonstrate a new way of analyzing the structure of a finite group by the properties and the number of conjugacy classes of its local subgroups.

In this article, we study Codazzi couplings of an arbitrary connection ∇ with a a nondegenerate 2-form !, an isomorphism L on the space of derivation of rho-commutative algebra A, which the important examples of isomorphism L are almost complex and almost para-complex structures, a metric g that (g; !;L) form a compatible triple. We study a statistical structure on rho-commutative algebras by the classical manner on Riemannian manifolds. Then by recalling the notions of almost (para-)Kähler rho-commutative algebras, we generalized the notion of Codazzi-(para-)Kähler rho-commutative algebra as a (para-)Kähler (or Fedosov) rho-commutative algebra which is at the same time statistical and moreover define the holomorphic rho-commutative algebras.

This paper is devoted to the study of a class of evolution inclusion in Banach spaces with nonlocal plus local mixed initial conditions. Under some mild assumptions, a unique solvability result to the multivalued evolution problem is obtained via the arguments of fixed point principle and the theory of $C^0$-semigroup.

‎Let $G=(V_G‎, ‎E_G)$ be a simple and connected graph‎. ‎A set $M\subseteq E_G$ is called a matching of‎ ‎$G$ if no two edges of $M$ are adjacent‎. ‎The number of edges in $M$ is called‎ ‎its size‎. ‎A matching $M$ is maximal if it cannot be extended to a larger‎ ‎matching in $G$‎. ‎The smallest size of a maximal matching is called the‎ ‎saturation number of $G$‎. ‎In this paper we are concerned with the saturation‎ ‎numbers of lexicographic product of graphs‎. ‎We also address and solve an open‎ ‎problem about the size of maximum matchings in graphs with a given maximum‎ ‎degree $\Delta$‎.

Some results on the sets of almost convergent, statistically convergent, uniformly statistically convergent, I-convergent subsequences of (sn) have been obtained by many authors via establishing a one-to-one correspondence between the interval (0, 1] and the collection of all subsequences of a given sequence s = (sn). However, there are still some gaps in the existing literature. In this paper we plan to fill some of the gaps with new results. Some of them are easily derived from earlier results but they offer some new deeper insights. © 2022, Hacettepe University. All rights reserved.

Let {\alpha} be a prime Hurwitz integer. H{\alpha}, which is the set of residual class with respect to related modulo function in the rings of Hurwitz integers, is a subset of H, which is the set of all Hurwitz integers. We consider left congruent module {\alpha} and, the domain of related modulo function in this study is ZN({\alpha}), which is residual class ring of ordinary integers with N({\alpha}) elements, which is the norm of prime Hurwitz integer {\alpha}. In this study, we present an algebraic construction technique, which is a modulo function formed depending on two modulo operations, for codes over Hurwitz integers. Thereby, we obtain the residue class rings of Hurwitz integers with N({\alpha}) size. In addition, we present some results for mathematical notations used in two modulo functions, and for the algebraic construction technique formed depending upon two modulo functions. Moreover, we present graphs obtained by graph layout methods, such as spring, high-dimensional, and spiral embedding, for the set of the residual class obtained with respect to the related modulo function in the rings of Hurwitz integers.

Let $R$ be a commutative ring with nonzero identity. An $R$-module $M$ is called $\phi$-P-flat if $x \in \Ann(s)M$ for every non-nilpotent element $s \in R$ and $x\in M$ such that $sx=0$. In this paper, we introduce and study the class of $\phi$-PF-rings, i.e., rings in which all ideals are $\phi$-P-flat. Among other results, the transfer of the $\phi$-PF-ring to the amalgamation is investigated. Several examples which delineate the concepts and results are provided.

The asymptotic equivalence of linear and quasilinear impulsive dynamic equations on time scales, as well as two types of linear equations, are proven under mild conditions. To establish the asymptotic equivalence of two impulsive dynamic equations a method has been developed that does not require restrictive conditions, such as the boundedness of the solutions. Not only the time scale extensions of former results have been obtained, but also improved for impulsive differential equations defined on the real line. Some illustrative examples are also provided, including an application to a generalized Duffing equation

Motivated by the results involving Drazin inverses of Patr\'{i}cio and Puystjens, we investigate the relevant results for pseudo Drazin invertibility and generalized Drazin invertibility in two semigroups of Banach algebras. Given a Banach algebra $\mathcal{A}$ and $e^2=e\in \mathcal{A}$, we first establish the relation between pseudo Drazin invertibility (resp., generalized Drazin invertibility) of elements in $e\mathcal{A}e$ and $e\mathcal{A}e+1-e$. Then this result leads to a remarkable behavior of pseudo Drazin invertibility (resp., generalized Drazin invertibility) between the operators in the semigroup $AA^{-}\mathscr{B}(X)AA^{-}+I_X-AA^{-}$ and the semigroup $A^{=}A\mathscr{B}(Y)A^{=}A+I_Y-A^{=}A$, where $A^{-}, A^{=}\in \mathscr{B}(Y,X)$ are inner inverses of $A\in \mathscr{B}(X,Y)$.

One of the most crucial parts of applying a regularization method to solve an ill-posed problem is choosing a regularization parameter to obtain an optimal order error estimate. In this paper, we consider the finite dimensional realization of the parameter choice strategy proposed in [C. Mekoth, S. George and P. Jidesh. Fractional Tikhonov regularization method in Hilbert scales. Appl. Math. Comput.(2021), 392: 125701, 26 DOI:10.1016/j.amc.2020.125701] for Fractional Tikhonov regularization method for linear ill-posed operator equations in the setting of Hilbert scales.

In this study, we aim to introduce the notion of fuzzy partial metric spaces which is a generalization of crisp partial metric spaces in the fuzzifying view with the distance between ordinary points. For this aim, we first present the concept of fuzzy partial metric spaces by considering the distance as non-negative, upper semi-continuous, normal and convex fuzzy numbers by giving examples. We obtain some useful inequalities under some restrictions in fuzzy partial metric spaces. Then we discuss the relationships with the other metric structures and we point out Banach's fixed point theorem as an application of the proposed properties and relations. Finally, we show that fuzzy partial metric spaces induce some $\alpha$-level topology, Lowen fuzzy topology, and fuzzifying topology.

This paper deals with the Catalan, Hankel, binomial transforms of the generalized bivariate Fibonacci and Lucas polynomials. Also, some useful results such as generating functions, Binet formulas, summations of transforms defined by using recurrence relations of these special polynomials are presented. Furthermore, certain important relations among these transforms are deduced by using obtained new formulas. Finally, the Catalan and Cassini formulas for these transforms are also derived.

The purpose of this paper is to present the relations among the completeness of sequences, of filters and of nets in the framework of fuzzy quasi-pseudometric spaces. In particular, we show that right completeness of filters and of sequences are equivalent under special conditions of fuzzy quasi-pseudometrics. By introducing a kind of more general right K-Cauchy nets in fuzzy quasi-pseudometric spaces, the equivalence between the completeness of the nets and the sequential completeness is established.

In this article, we prove some well-known coupled fixed point theorems in 0-complete metric spaces. Also, we present some corollaries related to our study. In addition to these, we give an example where our results successfully obtained the existence and uniqueness of the coupled fixed point, which cannot be applied to demonstrate in complete metric spaces. Finally, we apply our results to examine the existence and uniqueness of a solution of the system of nonlinear integral equations.

Let $\mathcal{A}$ denote the class of functions $f$ which are analytic in the open unit disk $\mathbb{U}$ and given by\[f(z)=z+\sum_{n=2}^{\infty }a_{n}z^{n}\qquad \left( z\in \mathbb{U}\right) .\]The coefficient functional $\phi _{\lambda }\left( f\right) =a_{3}-\lambda a_{2}^{2}$ on $f\in \mathcal{A}$ represents various geometric quantities. For example, $\phi _{1}\left( f\right) =a_{3}-a_{2}^{2}=S_{f}\left( 0\right) /6,$ where $S_{f}$ is the Schwarzian derivative. The problem of maximizing the absolute value of the functional $\phi _{\lambda }\left( f\right) $ is called the Fekete-Szegö problem.In a very recent paper, Shafiq \textit{et al}. [Symmetry 12:1043, 2020] defined a new subclass $\mathcal{SL}\left(k,q\right), (k>0, 0

We generalize the lower bound estimates for eigenvalues of the twisted Dirac operator on compact Riemannian Spinc−c−submanifold obtained by Roger Nakad and Julien Roth in (Archiv der Mathematik 104(5), 453-461, 2015).

In this paper, we use the concept of weak demicompactness in order to give some properties for the uniformly continuous cosine families. Our theoretical results will be illustrated by investigating the spectral inclusion for a uniformly continuous cosine family for an upper semi-Fredholm spectrum.

We find Ricci curvature bounds for pointwise semi-slant warped products submanifolds in non-Sasakian generalized Sasakian space forms in this work, and analyze the equality case of the inequality. The derived inequality is also used to develop a number of applications.

For a natural number $n\geq 2$, the function $\phi_{n\mathcal{L}}(z)=1+nz/(n+1)+z^n/(n+1)$ maps the open unit disk onto a domain bounded by an epicycloid with $(n-1)$ cusps. A class of starlike functions associated with $\phi_{n\mathcal{L}}$ is defined in the unit disk and its sharp bounds on initial coefficients, various inclusion relations and radii problems related to the other subclasses of starlike functions are investigated. As an application, the corresponding results are determined in the limiting case for the class of normalized analytic functions $f$ satisfying $|zf'(z)/f(z)-1

The multi-variable special matrix polynomials have been identified significantly both in mathematical and applied frameworks. Due to its usefulness and various applications, a variety of its extensions and generalizations have been investigated and presented. The purpose of the paper is intended to study and emerge with a new generalization of Hermite matrix based Sheffer polynomials by involving integral transforms and some known operational rules. Their properties and quasi-monomial nature are also established. Further, these sequences are expressed in determinant forms by utilizing the relationship between the Sheffer sequences and Riordan arrays. An analogous study of these results is also carried out for certain members belonging to generalized Hermite matrix based Sheffer polynomials.

In this paper we work with invertible skew pairings for weak bialgebras in a symmetric monoidal category where every idempotent morphism splits. We prove that this kind of skew pairings induces examples of weak distributive laws and therefore they provide weak wreath products. Also we will show that they define weakly comonoidal mutually weak inverse pairs of weak distributive laws and, by the results proved by G. Böhm and J. Gómez-Torrecillas, we obtain weak wreath products that become weak bialgebras with respect to the tensor product coalgebra structure. As an application, we will show that the Drinfel'd double of a finite weak Hopf algebra can be constructed using the weak wreath product associated to an invertible $1$-skew pairing.

The present paper is devoted to the duality theory for the convex optimal control problem of second-order differential inclusions with periodic boundary conditions. First, we use an auxiliary problem with second-order discrete-approximate inclusions and focus on formulating sufficient conditions of optimality for the differential problem. Then, we concentrate on the duality that exists in periodic boundary conditions to establish a dual problem for the differential problem and prove that Euler-Lagrange inclusions are duality relations for both primal and dual problems. Finally, we consider an example of the duality for the second-order linear optimal control problem.

A basic assumption of the classic reinsurance model is that the distribution of the loss is precisely known. In practice, only partial information is available for the loss distribution due to the lack of data and estimation error. We study a distributionally robust reinsurance problem by minimizing the maximum Value-at-Risk (or the worst-case VaR) of the total retained loss of the insurer for all loss distributions with known mean and variance. Our model handles typical stop-loss reinsurance contracts. We show that a three-point distribution achieves the worst-case VaR of the total retained loss of the insurer, from which the closed-form solutions of the worst-case distribution and optimal deductible are obtained. Moreover, we show that the worst-case Conditional Value-at-Risk of the total retained loss of the insurer is equal to the worst-case VaR, and thus the optimal deductible is the same in both cases.

In this paper, for the mapping of a sphere into a compact orientable manifold S n → M , n ⩾ 1 , we solve the problem of determining whether it represents a nontrivial element in the homotopy group of the manifold π n ( M ) πn(M ). For this purpose, we consistently use the theory of iterated integrals developed by K.-T. Chen. It should be noted that the iterated integrals as repeated integration were previously meaningfully used by Lappo-Danilevsky to represent solutions of systems of linear differential equations and by Whitehead for the analytical description of the Hopf invariant for mappings f : S 2 n - 1 → S n , n ⩾ 2 . We give a brief description of Chen’s theory, representing Whitehead’s and Haefliger’s formulas for the Hopf invariant and generalized Hopf invariant. Examples of calculating these invariants using the technique of iterated integrals are given. Further, it is shown how one can detect any element of the fundamental group of a Riemann surface using iterated integrals of holomorphic forms. This required to prove that the intersection of the terms of the lower central series of the fundamental group of a Riemann surface is a unit group.