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We prove a theorem that generalizes Schmidt's Subspace Theorem in the context of metric diophantine approximation. To do so we reformulate the Subspace Theorem in the framework of homogeneous dynamics by introducing and studying a slope formalism and the corresponding notion of semistability for diagonal flows. [ABSTRACT FROM AUTHOR]

In this paper, we study the uniqueness of meromorphic functions with q-shift difference-differential polynomials F = [P(f)L(z, f)s](k) and G = [P(g)L(z, g)s](k), where P(z) is a non-constant polynomial with degree n sharing a finite value. The results of this paper are an extension of the previous theorems given by Harina P. Waghamore and Rajeshwari S [19]. [ABSTRACT FROM AUTHOR]

In the present article, we provide a new nonlinear contraction for the Schauder type selections of multi-valued mappings in metric spaces which is a new spread of the Darbo theorem. Meanwhile, we apply the main results in coupled fixedpoint theory and functional integral equation. [ABSTRACT FROM AUTHOR]

The productivity and efficiency of universities were analysed in this study. The data and results of the Entrepreneurial and Innovative University Index-EIUI, which is calculated by TÜBITAK every year by considering various information for universities, were used. The study aimed to discuss the index, productivity, and efficiency results comparatively. Four-year data (2019-2022) and the index values were used. Balanced panel data analysis was performed on universities consistently included in the list each year. In the calculation of the index, a weighted sum of values standardized by the min-max method was taken into account. This is available in the calculation methodology of the index. Total factor productivity and stochastic frontier model methods were used for the analysis of productivity and efficiency, respectively. Universities that enter the index list every year and are at the top are effective, but they could not increase their productivity in the previous years. Universities established before 1992 may have approached the saturation level in terms of the input-output relationship, but it can be said that they can maintain their effectiveness. Some public and private universities that were established in 1992 and later have raised their productivity and efficiency. Although the index value and efficiency values overlapped to a certain extent, the significant differences in productivity were remarkable. While the studies in the literature focused on the meta-analysis of the index and the efficiency analysis of universities with various methods, this study presented an inclusive and comparative analysis in terms of index, productivity, and efficiency with panel data analysis. [ABSTRACT FROM AUTHOR]

This study presents all solutions to the Diophantine equations Fk=LmLn and Lk=FmFn. To be clear, the Fibonacci numbers that are the product of two arbitrary Lucas numbers and the Lucas numbers that are the product of two arbitrary Fibonacci numbers are determined herein. The results under consideration are proven by using the Dujella-Pethő lemma in coordination with Matveev's theorem. All common terms of the Fibonacci and Lucas numbers are determined. Further, the Lucas-square Fibonacci and Fibonacci-square Lucas numbers are given. [ABSTRACT FROM AUTHOR]

In this study, we define the binomial transforms of third-order Jacobsthal and modified third-order Jacobsthal polynomials. Further, the generating functions, Binet formulas and summation of these binomial transforms are found by recurrence relations. Also, we establish the relations between these transforms by deriving new formulas. Finally, the Vajda, d'Ocagne, Catalan and Cassini formulas for these transforms are obtained. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the existence of multiple positive symmetric solutions for fourth order p-Laplacian iterative system with integral boundary conditions. Initially, we establish the existence of at least one and two positive symmetric solutions for the fourth order problem using Krasnosel'skii fixed point theorem. Subsequently, we establish the existence of at least three positive symmetric solutions by applying fivefunctionals fixed point theorem. [ABSTRACT FROM AUTHOR]

The manuscript is an attempt to consider all methods which are applicable to investigation a directional index for composition of an analytic function in some domain and an entire function. The approaches are applied to find sufficient conditions of the L-index boundedness in a direction b 2 Cn n f0g, where the continuous function L satisfies some growth condition and the condition of positivity in the unit polydisc. The investigation is based on a counterpart of the Hayman Theorem for the class of analytic functions in the polydisc and a counterpart of logarithmic criterion describing local conduct of logarithmic derivative modulus outside some neighborhoods of zeros. The established results are new advances for the functions analytic in the polydisc and in multidimensional value distribution theory. [ABSTRACT FROM AUTHOR]

Discrete-time systems are sometimes used to explain natural phenomena that happen in nonlinear sciences. We study the periodicity, boundedness, oscillation, stability, and certain exact solutions of nonlinear difference equations in this paper. Using the standard iteration method, exact solutions are obtained. Some well-known theorems are used to test the stability of the equilibrium points. Some numerical examples are also provided to confirm the theoretical work's validity. The numerical component is implemented with Wolfram Mathematica. The method presented may be simply applied to other rational recursive issues. In this paper, we explore the dynamics of adhering to a rational difference formula -xn+1 = xn􀀀29 -1-xn􀀀5xn􀀀11xn􀀀17xn􀀀23xn􀀀29, where the initials are arbitrary nonzero real numbers. [ABSTRACT FROM AUTHOR]

In this paper, a class of fractional multiobjective interval valued optimization problems with Einvexity is considered. First, the definition of the E-invex fractional interval value function is given under the interval order relation, and the existence of these fractional interval-valued functions is verified by examples. Second, we present the E-KKT necessary optimality conditions and the sufficient optimality conditions for a fractional interval-valued optimization problem (FIVPE) under E-invexity. Last, the Mond-Weir E-dual problem (DFIVPE) of (FIVPE) is established, and several E-duality theorems are obtained under E-invexity. To some extent, this paper generalizes the existing relevant results obtained recently. [ABSTRACT FROM AUTHOR]

In this paper, we study neutrosophic hesitant fuzzy ideal. We introduce the notions of neutrosophic hesitant fuzzy primary ideal, neutrosophic hesitant fuzzy semiprimary ideal of a ring and discussion of some important theorems and results. [ABSTRACT FROM AUTHOR]

In this research, new representations of basic functions are proposed based on the new types of fuzzy partition and a subnormal generating function. The generalized uniform fuzzy partitions in subnormal case, i.e. in case a generating function K is not normal (generalized normal case), and simpler form of fuzzy transform (FzT) components based on these new representations of the generalized uniform fuzzy partitions are indicated. The main properties of a new uniform fuzzy partition are suggested. New theorems and lemmas are proved. [ABSTRACT FROM AUTHOR]

Using quantization techniques, we show that the ı-invariant of Fujita-Odaka coincides with the optimal exponent in a certain Moser-Trudinger type inequality. Consequently, we obtain a uniform Yau-Tian-Donaldson theorem for the existence of twisted Kähler-Einstein metrics with arbitrary polarizations. Our approach mainly uses pluripotential theory, which does not involve Cheeger-Colding-Tian theory or the non-Archimedean language. A new computable criterion for the existence of constant scalar curvature Kähler metrics is also given. [ABSTRACT FROM AUTHOR]

In Part III of Anarchy, State, and Utopia (1974), Robert Nozick presents what he calls 'the model of possible worlds' (307) to examine the formal properties of utopia, defined as 'the best of all possible worlds' (298). The basic idea is that each person is given the power to create any possible world and its inhabitants by imagining them. Two definitions of stability have been proposed: (a) the non-circular definition according to which a world is stable if and only if nobody can imagine a better world and (b) the circular definition according to which a world is stable if and only if nobody can imagine a better world that is also stable. In this paper, we prove four theorems (namely, the indeterminacy theorem, the stable dystopia theorem, the nobody's utopia theorem and the redundancy theorem) that provide us with decisive reasons to reject the circular definition and opt for the non-circular definition of stability to analyse Nozick's theory of utopia. [ABSTRACT FROM AUTHOR]

We show that there is a simple derivation of triviality with very few assumptions involving the formula that the negated conditional entails the antecedent of the conditional. [ABSTRACT FROM AUTHOR]

A double Italian dominating (DID) function of a graph G = (V, E) is a function f : V (G) → {0, 1, 2, 3} having the property that for every vertex v ∈ V, Pu∈NG[v] f(u) ≥ 3, if f(v) ∈ {0, 1}. A restrained double Italian dominating (RDID) function is a DID function f such that the subgraph induced by the vertices with label 0 has no isolated vertex. A total restrained double Italian dominating (TRDID) function is an RDID function f such that the set {v ∈ V : f(v) > 0} induces a subgraph with no isolated vertex. We initiate the study of TRDID function of any graph G. The TRDID and RDID functions of the middle of any graph G are investigated, and then, the sharp bounds for these parameters are established. Finally, for a graph H, we provide the minimum value of TRDID and RDID functions for corona graphs, H ◦ K1, H ◦ K2 and middle of them. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of the cohomological dimension filtration with respect to a system of ideals. In particular, a characterization of cohomological dimension filtration of a module by the associated prime ideals of its factors is established. As a main result, we provide a necessary and sufficient condition for an ascending chain of submodules of an R -module M to be the cd-filtration of M, with respect to a system of ideals. [ABSTRACT FROM AUTHOR]

The comaximal intersection graph CI(R) of ideals of a ring R is an undirected graph whose vertex set is the collection of all non-trivial (left) ideals of R and any two vertices I and J are adjacent if and only if I + J = R and I ∩ J 6= 0. We study the connectedness of CI(R). We also discuss independence number, clique number, domination number, chromatic number of CI(R). [ABSTRACT FROM AUTHOR]

In this paper the zero forcing number as well as propagation time of Cay(G, Ω), where G is a finite group and Ω ⊂ G\{1} is an inverse closed generator set of G is studied. In particular, it is shown that the propagation time of Cay(G, Ω) is at most two for some special generators. [ABSTRACT FROM AUTHOR]

Let R be a prime ring and Z(R) denotes the center of R. In this study, we expose the commutativity of R as a consequence of specific differential identities involving derivations acting on left ideals of R. Finally, we give examples that demonstrate the necessity of hypotheses taken in the theorems. [ABSTRACT FROM AUTHOR]

This study establishes various summation formulas involving harmonic and generalized harmonic numbers, as well as binomial coefficients. Additionally, several finite series identities and their limits related to H2k, H(2)2k and Ok are derived as specific instances. [ABSTRACT FROM AUTHOR]

Suppose p is a prime and T is a non-identity Sylow p -subgroup of a finite group G for which C G (O p (G)) ⩽ O p (G). D. Bundy, N. Hebbinghaus, and B. Stellmacher determined the structure of G in an important case in which C G (Ω 1 (Z (T))) and N G (B e (T)) generate a proper subgroup of G , where B e (T) is the Baumann subgroup of T according to a particular definition. We apply their theorem to prove an analogous theorem that uses a different definition of the Baumann subgroup. This result is applied in a related article to prove a transfer theorem for odd primes. [ABSTRACT FROM AUTHOR]

We present a refined, simplified, and unified proof of Aristarchus' inequality, without resorting to trigonometry, calculus or extended geometric arguments. [ABSTRACT FROM AUTHOR]

We prove two theorems about the circular Apollonian packing. The first states that the circles used in the packing have an infinite total length. The second states that the largest circle is covered by the other circles used in the packing, up to an area of Lebesgue measure zero. Our proofs are elementary and only use basic coordinate geometry. [ABSTRACT FROM AUTHOR]

We give short proofs that ℝ is uncountable directly from the definition of ℝ as the set of Dedekind cuts of ℚ. [ABSTRACT FROM AUTHOR]

Fuzzy field and arithmetic operators based on transmission average (TA) and neutral member are dealt by Abbasi et al. [1]. Many examples are exist such that based on their definition ...) is not equal to .... Therefore, we investigate the conditions that .... Numerical examples show the applicability of theorems and mentioned problems. [ABSTRACT FROM AUTHOR]

We discuss a phenomenological self-consistent model of a turbulent magnetized conducting fluid for mean flow and magnetic field in geophysical and astrophysical contexts. This model is designed to study spirality and dynamo effect in the study of astro-geophysical magnetic fields. It is believed that the very existence of cosmic magnetic fields is largely explained by the chirality of background turbulence, the simplest measure of which is the non-vanishing helicity of small-scale turbulence. The mean velocity and magnetic fields are modelled using averaged MHD-equations and phenomenological differential equations for the four bulk turbulence quantities (hydro magnetic turbulent energy, magnetic and cross helicity and residual helicity). These model equations, combined with the mean-field equations, allow the most complete construction of a self-consistent model of the turbulent dynamo. These problems and open questions are considered, especially those concerning the model transport equations for the determination of the alpha effect in astrophysical magnetic fields. The presented work is mainly aimed at modelling rotation effects in hydro magnetic turbulent flows of spiral space and thermonuclear plasma. [ABSTRACT FROM AUTHOR]

A model of two-velocity multiphase medium with equal phase pressures was investigated. Two pulse equations were used where interphase force has a stabilizing term depending on flow parameters gradient. Phases were assumed incompressible. It was shown that this asssumption does not have any impact on the main conclusions while the model is significantly simplified. One does not need any energy equations because the movement does not depend on phase temperatures. Two differential equations describing relative phase movement were derived. Each of the two differential equations describing relative phase movement leads to its own wave velocity. For a steady-state stable transition when the mixture parameters do not change with time in some coordinate system (a steady-state or automodel flow) wave velocity must be equal for all the differential equations. This gives a condition for calculation of the stabilizing term. We defined conditions for continuous transition from one state to another as well as conditions when this transition can be only discontinuous. Analytical solutions helped us to find stabilizing term for interphase friction force (the only posssible in the corresponding class). [ABSTRACT FROM AUTHOR]

In this paper we extend some previously known results in the unit ball and in the unit disk on Bergman projections in bounded strongly pseudoconvex domains and in tubular domains over symmetric cones. It should be also added that on the other hand all our new results are also related with analytic spaces in product domains. Below first we give some definitions and basic lemmas and facts on bounded strongly pseudoconvex domains and then in tubular domains over symmetric cones. [ABSTRACT FROM AUTHOR]

In this note, we introduce a new convolution identity for the difference between classical Fibonacci numbers Fk and the alternating powers of k. We then apply this identity to develop a direct formula for the alternating convolution of Fibonacci numbers Fk and powers of k. Finally, we obtain an explicit formula for the alternating weighted Brousseau sums of the Fibonacci numbers using this alternating convolution identity. Furthermore, we generalize these identities to the Gibonacci numbers Gk with arbitrary initial values. [ABSTRACT FROM AUTHOR]

In this study, we define the k-Leonardo, k-Leonardo-Lucas, and Modified k-Leonardo sequences, and some terms of these sequences are given. Then, we obtain the generating functions, summation formulas, etc. Also, we obtain the Binet formulas in three different ways. The first is in the known classical way, the second is with the help of the sequence's generating functions, and the third is with the help of the matrices. In addition, we examine the relations between the terms of the κ-Leonardo, κ-Leonardo-Lucas, Modified k-Leonardo, Leonardo, Leonardo-Lucas, Modified Leonardo, Francois, Fibonacci, and Lucas sequences. Moreover, we associate the terms of these sequences with matrices. Furthermore, we present on the application of these sequences to hyperbolic quaternions. For these quaternions, we give many properties such as Binet formulas. Finally, the terms of the κ-Leonardo, κ-Leonardo-Lucas, and Modified k-Leonardo sequences are associated with their hyperbolic quaternion values. [ABSTRACT FROM AUTHOR]

This paper contains a heuristic presentation of a new method for testing whether the mapping f from a simply connected domain O from compactified n-dimensional Euclidean space to compactified n-dimensional Euclidean space, is constant or when it has a good boundary property. Namely, two theorems have been proved which show that the mapping will be constant or have some good boundary property depending on where the fixed points and points of attraction of the continuous automorphism g of domain O, which generates the cyclic group with respect to which f is normal, are located. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new iterative scheme to approximate the fixed point of generalized α-nonexpansive mappings. we first prove that the proposed iteration process is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas and Thakur processes for contractive mappings. We also obtain some weak and strong convergence theorems for generalized α-nonexpansive mappings. Using the example presented in [R. Pant and R. Shukla, Approximating fixed point of generalized α-nonexpansive mappings in Banach spaces, J. Numer. Funct. Anal. Optim. 38(2017) 248-266.], we compare the convergence behavior of the new iterative process with other iterative processes. [ABSTRACT FROM AUTHOR]

In this article, we present the notion of Single-Valued Pentapartitioned Neutrosophic Bi-Topological Space (SVPNBTS) as a generalization of Single-Valued Pentapartitioned Neutrosophic Topological Space (SVPNTS) and Neutrosophic Bi-Topological Space (NBTS). Besides, we study the different types of open set and closed set namely single-valued pentapartitioned neutrosophic bi-open set (SVPNBOS), single-valued pentapartitioned neutrosophic bi-closed set (SVPNBCS), single-valued pentapartitioned neutrosophic bi-semi-open set (SVPNBSOS), single-valued pentapartitioned neutrosophic bi-semi-closed set (SVPNBSCS), single-valued pentapartitioned neutrosophic bi-pre-open set (SVPNBPOS), single-valued pentapartitioned neutrosophic bi-preclosed set (SVPNBPCS), single-valued pentapartitioned neutrosophic bi-b-open set (SVPNBb-OS), singlevalued pentapartitioned neutrosophic bi-b-closed set (SVPNBb-CS), etc. via SVPNBTSs. Besides, we introduce the notion of pairwise SVPNOS, pairwise SVPNCS, pairwise SVPNSOS, pairwise SVPNSCS, pairwise SVPNPOS, pairwise SVPNPCS, pairwise SVPNb-OS, pairwise SVPNb-CS, and furnish few illustrative examples on them. Further, we investigate several properties of these classes of sets and prove some interesting results in the form of propositions, theorems, etc. via SVPNBTSs. [ABSTRACT FROM AUTHOR]

A non-parallel submodules graph of M, denoted by G ∦ (M), is an undirected simple graph whose vertices are in one-to-one correspondence with all non-zero proper submodules of M and two distinct vertices are adjacent if and only if they are not parallel to each other. In this paper, we investigate the interplay between some of the module-theoretic properties of M and the graph-theoretic properties of G ∦ (M). It is shown that if G ∦ (M) is connected, then diam(G ∦ (M)) ≤ 3 and if G ∦ (M) is not connected, then G ∦ (M) is a null graph. It is proved that G ∦ (M) is null if and only if M contains a unique simple submodule. In particular, M is a strongly semisimple R -module if and only if G ∦ (M) is a complete graph, and from this it follows that if G ∦ (M) is complete, then every R-module with finite Goldie dimension is Artinian and Noetherian. In addition, G ∦ (M) is a finite star graph if and only if M∼= Zpq, for some distinct prime numbers p and q. [ABSTRACT FROM AUTHOR]

In this note, we intend to explain and interpret the proofs of some of the classic mathematical results that are made easy by the beautiful mind of Karamzadeh, who has an incredible love for mathematics and has been enthusiastically busy for years with regard to its popularization. Concerning the latter comment, the general readers are the primary focus of our attention. [ABSTRACT FROM AUTHOR]

This paper is concerned with a nonlinear higher-order Kirchhoff-type equation with dissipation in a bounded domain. By establishing a first order differential inequality technique, a lower bound for the blow-up time is obtained when the blow-up of solution occurs. [ABSTRACT FROM AUTHOR]

In this paper, using fixed point method, we investigate the stability and also the superstability of cubic bi-derivations on Banach algebras. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to prove several majorization type inequalities using Green and 4-convex functions. First of all, we drive generalized majorization inequality for arbitrary n-tuples and real weights. Further, we explore the inequality for majorized tuples, weighted majorization theorems given by Fuchs, Dragomir and Maligranda et al. For deriving another generalized majorization inequality, we use a simple form of Jensen's inequality, and by similar fashion we apply classical earlier majorization theorems for further elaborations of generalized inequality. Several applications of information theory are discussed at the end of the article. [ABSTRACT FROM AUTHOR]

In this paper we provide new refinements of Aczel-type inequality and give some applications. Furthermore, we show that two of three theorems in the work by J. Tian and M.-H. Ha (J. Math. Inequal. 12 (1) (2018), 175-189) are incorrect whereas the proof of the other is technically wrong. We establish an improvement of the correctly stated theorem with a simple proof and give counterexamples to the wrong ones. [ABSTRACT FROM AUTHOR]

In this note, we establish a bijection between two kinds of subsets of the set of all partitions of n by extending Chapman's conjugation of 2-modular diagrams. Based on this bijection, we provide a combinatorial proof of the q-binomial theorem. [ABSTRACT FROM AUTHOR]

We use properties of a cyclic quadrilateral to find the inradius of an arbelos. [ABSTRACT FROM AUTHOR]

The principle of subordination is useful in comparing two holomorphic functions when the range of one holomorphic function is a subset of the other and they comply at a single point. The subordination, when spoken in fuzzy set theory, becomes fuzzy subordination as the comparison between two holomorphic functions is made using the fuzzy membership function. In this article, differential and fuzzy differential Subordination, superordination, and sandwich theorems have been discussed for the classes defined by using q-derivative and symmetric q-derivative operators. [ABSTRACT FROM AUTHOR]

I show that Wittgenstein's critique of G.H. Hardy's mathematical realism naturally extends to Paul Benacerraf's influential paper, 'Mathematical Truth'. Wittgenstein accuses Hardy of hastily analogizing mathematical and empirical propositions, thus leading to a picture of mathematical reality that is somehow akin to empirical reality despite the many puzzles this creates. Since Benacerraf relies on that very same analogy to raise problems about mathematical 'truth' and the alleged 'reality' to which it corresponds, his major argument falls prey to the same critique. The problematic pictures of mathematical reality suggested by Hardy and Benacerraf can be avoided, according to Wittgenstein, by disrupting the analogy that gives rise to them. I show why Tarskian updates to our conception of 'truth' discussed by Benacerraf do not answer Wittgenstein's concerns. That is, because they merely presuppose what Wittgenstein puts into question, namely, the essential uniformity of 'truth' and 'proposition' in ordinary discourse. [ABSTRACT FROM AUTHOR]

We study the limit of fluctuations of the rescaled occupation time process of a branching particle system in Rd, where the particles are subject to symmetric a-stable migration (0 < a = 2), critical binary branching, and general non-lattice lifetime distribution. We focus on two different regimes: lifetime distributions having finite expectation, and Pareto-type lifetime distributions, i.e. distributions belonging to the normal domain of attraction of a γ-stable law with γ ∈ (0, 1). In the latter case we show that, for dimensions aγ < d < a(1 + γ), the fluctuations of the rescaled occupation time converge weakly to a centered Gaussian process whose covariance function is explicitly calculated, and we call it weighted sub-fractional Brownian motion. Moreover, in the case of lifetimes with finite mean, we show that for a < d < 2a the fluctuation limit turns out to be the same as in the case of exponentially distributed lifetimes studied by Bojdecki et al. (2004, 2006a,b). We also investigate the maximal parameter range allowing existence of the weighted sub-fractional Brownian motion and provide some of its fundamental properties, such as path continuity, long-range dependence, self-similarity and the lack of Markov property. [ABSTRACT FROM AUTHOR]

Let G be a closed symmetric monoidal concrete Grothendieck category. In this paper, we introduce a model structure on (CN(G),P⊗ dw) the exact category of N-complexes with the degree-wise ⊗-pure exact structure. Our result is based on the Gillespie's Theorem by introducing two compatible cotorsion pairs on this category. [ABSTRACT FROM AUTHOR]

A theorem of Arens and Calderon states that if A is a commutative Banach algebra with Jacobson radical Rad(A), and if a0,..., an ∈ A with a0 2 Rad(A) and a1 an invertible element of A, then there exists y ∈ Rad(A) such that ... n this paper, we give extensions of this result to commutative non-normed topological algebras, as this is vital for extending an embedding theorem of Allan in [2] regarding the embedding of the formal power series algebra C[[X]] into a commutative Banach algebra. [ABSTRACT FROM AUTHOR]

A progress report on the (still unresolved) Landsberg-Berwald problem of Finsler geometry: whether there can be non-Berwaldian regular Landsberg spaces. [ABSTRACT FROM AUTHOR]

The main aim of this research is to investigate the stability of a functional equation that maintains the lattice structure in a uniformly complete unital Banach f -algebra. Through this inquiry, we can shed light on the behavior of this equation and its relationship with the algebraic properties of a Banach space. This research has both theoretical and practical implications. It contributes to the foundations of functional analysis, lattice theory, operator theory, approximation theory, and various applied mathematical disciplines. The findings from this research can have implications in diverse fields ranging from mathematics and physics to engineering and computer science, offering valuable insights and potential applications. [ABSTRACT FROM AUTHOR]