Equivalent Statements Research Articles

Why Do People Agree With Both Regular and Reversed Items? A Logical Response Perspective.

The current research challenges the received view that misresponses to reversed items are the result of participants' irrational behavior. On the contrary, for participants at a midpoint level of a trait, it is perfectly logical to agree and disagree with seemingly equivalent statements (e.g., I'm not tall, but neither am I short). For this reason, regular and reversed items for a unidimensional construct were predicted to load on separate factors. Two types of reversed items-polar opposites and negated regular items-were also predicted to load on separate factors, as they are qualitatively different. An empirical study supported this explanation. Differential responding was found to be highest for participants at the mid-level of a trait and diminished toward the ends, revealing a quadratic relationship and a trait × method interaction. Thus, our findings demonstrate that the logical response pattern of individuals at the mid-level of a trait is another previously unrecognized explanation for why the inclusion of regular and reverse-keyed items can contribute to the apparent bi-dimensionality of unidimensional constructs (for data analysis results, see https://osf.io/krh2w/).

On a reverse Mulholland-type inequality in the whole plane with general homogeneous kernel

By using the idea of introducing parameters and weight coefficients, a new reverse discrete Mulholland-type inequality in the whole plane with general homogeneous kernel is given, which is an extension of the reverse Mulholland inequality. The equivalent forms are obtained. The equivalent statements of the best possible constant factor related to several parameters and a few applied examples are presented.

A Hilbert-Type Integral Inequality in the Whole Plane Related to the Arc Tangent Function

In this work we establish a few equivalent statements of a Hilbert-type integral inequality in the whole plane related to the kernel of the arc tangent function. We prove that the constant factor, which is associated with the cosine function, is optimal. Some special cases as well as some operator expressions are also presented.

On a more accurate Hilbert-type inequality in the whole plane with the general homogeneous kernel

By the use of the weight coefficients, the idea of introduced parameters and the technique of real analysis, a more accurate Hilbert-type inequality in the whole plane with the general homogeneous kernel is given, which is an extension of the more accurate Hardy–Hilbert’s inequality. An equivalent form is obtained. The equivalent statements of the best possible constant factor related to several parameters, the operator expressions and a few particular cases are considered.

A new reverse Mulholland-type inequality with multi-parameters

<abstract> In this paper, we present a new reverse Mulholland-type inequality with multi-parameters and deal with its equivalent forms. Based on the obtained inequalities, the equivalent statements of the best possible constant factor related to several parameters are discussed. As an application, some interesting inequalities for double series are derived from the special cases of our main results. </abstract>

ON A NEW HILBERT-TYPE INEQUALITY IN THE WHOLE PLANE WITH THE GENERAL HOMOGENEOUS KERNEL

<abstract> By means of the weight coefficients and the idea of introducing parameters, a new discrete Hilbert -type inequality in the whole plane with the general homogeneous kernel is given, which is an extension of Hardy-Hilbert's inequality. The equivalent form is obtained. The equivalent statements of the best possible constant factor related to several parameters, the operator expressions and a few particular cases are considered. </abstract>

Mixed Type Hermite–Padé Approximants for a Nikishin System

We consider the problem of mixed type Hermite–Pade approximants and prove that the Nikishin system is perfect for this problem. Using the method of a vector equilibrium problem, we find weak asymptotics and prove the convergence of the approximants along any rays in the index table. We also present an equivalent statement in the form of a matrix Riemann–Hilbert problem.

A reverse Hardy\u2013Hilbert-type integral inequality involving one derivative function

In this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented.

Convex cones in mapping spaces between matrix algebras

We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The duals of such convex cones can be characterized in terms of ampliation maps, which can also be used to characterize many notions from quantum information theory—such as separability, entanglement-breaking maps, Schmidt numbers, as well as decomposable maps and k-positive maps in functional analysis. In fact, such characterizations hold if and only if the involved cone is a one-sided mapping cone. Through this analysis, we obtain mapping properties for compositions of cones from which we also obtain several equivalent statements of the PPT (positive partial transpose) square conjecture.

On Parseval’s Identity and Plancherel Relation in 2-Inner Product Spaces

This paper investigates the foundational concepts of linear 2-normed spaces and 2-inner product spaces, presenting essential definitions and theorems that elucidate their structure. We establish Parseval’s identity for finite orthonormal sets within these spaces and examine its relationship with the Plancherel relation. Our findings include theorems related to orthonormal sets and Bessel's inequality, highlighting their implications for countably infinite orthonormal sets. By contributing to the theoretical framework of 2-inner product spaces, we enhance the understanding of orthogonality and summability in this context. Introduced by Diminnie et al. (1973), the 2-inner product extends traditional inner product notions into a two-dimensional framework, offering valuable insights into unique mathematical structures. Recent contributions, such as the formalization of orthonormal sets by Elumalai and Patricia (2000) and the rigorous proofs of the Riesz theorems by Harikrishnan et al. (2011), further deepen our understanding of these spaces. This paper aims to develop important inequalities based on orthonormal sets and present equivalent statements related to them, fostering continued research in various mathematical contexts.

Acyclic Complexes and Gorenstein Rings

For a given class of modules [Formula: see text], let [Formula: see text] be the class of exact complexes having all cycles in [Formula: see text], and dw([Formula: see text]) the class of complexes with all components in [Formula: see text]. Denote by [Formula: see text][Formula: see text] the class of Gorenstein injective R-modules. We prove that the following are equivalent over any ring R: every exact complex of injective modules is totally acyclic; every exact complex of Gorenstein injective modules is in [Formula: see text]; every complex in dw([Formula: see text][Formula: see text]) is dg-Gorenstein injective. The analogous result for complexes of flat and Gorenstein flat modules also holds over arbitrary rings. If the ring is n-perfect for some integer n ≥ 0, the three equivalent statements for flat and Gorenstein flat modules are equivalent with their counterparts for projective and projectively coresolved Gorenstein flat modules. We also prove the following characterization of Gorenstein rings. Let R be a commutative coherent ring; then the following are equivalent: (1) every exact complex of FP-injective modules has all its cycles Ding injective modules; (2) every exact complex of flat modules is F-totally acyclic, and every R-module M such that M+ is Gorenstein flat is Ding injective; (3) every exact complex of injectives has all its cycles Ding injective modules and every R-module M such that M+ is Gorenstein flat is Ding injective. If R has finite Krull dimension, statements (1)–(3) are equivalent to (4) R is a Gorenstein ring (in the sense of Iwanaga).

On Hyperbolic Affine Generalized Infinite Iterated Function Systems

The aim of this paper is to provide alternative characterizations of hyperbolic affine generalized infinite iterated function systems. More precisely, we prove that, for such a system $${\mathcal {F}}=((X,\left\| .\right\| ),(f_{i})_{i\in I})$$ , among others, the following statements are equivalent: (a) $${\mathcal {F}}$$ is hyperbolic. (b) $$ {\mathcal {F}}$$ has attractor. (c) $${\mathcal {F}}$$ is strictly topologically contractive. (d) $${\mathcal {F}}$$ is uniformly point-fibred. In this way we generalize the result from the paper by Miculescu and Mihail (J Math Anal Appl 407:56–68, 2013). More equivalent statements are given for the particular case when I is finite and X is finite dimensional.

Arap Dilinin Yapısından Kaynaklanan Çeviri Zorlukları

Çeviri, insanlık tarihi boyunca toplumların bilimsel, kültürel, edebî, diplomatik vs. nedenlerle başvurduğu bir yoldur. Toplumlar ve diller arasındaki etkileşim, bir topluma veya dile ait zenginliğin diğerine aktarılması kanalıyla etkin bir şekilde sağlanmıştır. Çeviri eyleminin kendine has kural ve yöntemleri olmakla beraber birtakım zorlukları da vardır. Bu çalışmada daha çok çeviri deneyimi çerçevesinde karşılaşılan zorluklar ele alınmıştır. Çalışmada ele alınan yapısal zorlukların başında okuma zorluğu gelmektedir. Bilindiği gibi Arap Dilinde hareke kullanımı bazı metinler dışında hemen hemen yok gibidir. Bu durum sessiz harflerin okunmasını zorlaştırmakta, doğru anlam ve doğru çevirinin önünde bir engel oluşturmaktadır. Dilbilgisi kaynaklı zorluklar da çeviri zorluklarına sebebiyet vermektedir. İyi düzeyde gramer bilgisine sahip olanlar bile dilbilgisi kaynaklı zorluklarla karşılaşabilmektedir. Arapça i’râb kurallarının teorik düzeyden pratik düzeye aktarılması ve bol metin deneyimi zorlukların aşılmasına yardımcı olacaktır. Bu zorluklar örnek cümle ve metinlerle izah edilmiş, söz konusu cümlelerin tercümeleriyle ilgili öneriler sunulmuştur. Eşdeğer ifadeler bulunmaya çalışılmıştır. Kaynak dil ile hedef dil arasındaki dil yapısı, kültür, üslup vs. gibi farklılıklar eşdeğer çeviri imkânlarını kısıtlamaktadır. Diller ve kültürler arasındaki tüm bu farklılıklara rağmen eşdeğer çeviri imkânları gösterilmeye çalışılmıştır. Dillerin kendine özgü yapısından, çevirmenin bizzat kendisinden yahut iki dilin sahip olduğu kültürel farklılıklardan dolayı çeviri işleminde birtakım zorluklar yaşanabilir. Çevirmen her iki dilin de özelliklerine son derece hâkim olmalıdır. Böylece çeviri esnasında ortaya çıkan bu sorunların üstesinden gelecektir.

A New Extension of Hardy-Hilbert’s Inequality Containing Kernel of Double Power Functions

In this paper, we provide a new extension of Hardy-Hilbert’s inequality with the kernel consisting of double power functions and derive its equivalent forms. The obtained inequalities are then further discussed regarding the equivalent statements of the best possible constant factor related to several parameters. The operator expressions of the extended Hardy-Hilbert’s inequality are also considered.

Mathematical Representation of Clausius’ and Kelvin’s Statements of the Second Law and Irreversibility

We provide a stochastic mathematical representation for Clausius' and Kelvin-Planck's statements of the Second Law of Thermodynamics in terms of the entropy productions of a finite, compact driven Markov system and its lift. A surjective map is rigorously established through the lift when the state space is either a discrete graph or a continuous n-dimensional torus T^n. The corresponding lifted processes have detailed balance thus a natural potential function but no stationary probability. We show that in the long-time limit the entropy production of the finite driven system precisely equals the potential energy decrease in the lifted system. This theorem provides a dynamic foundation for the two equivalent statements of Second Law of Thermodynamics, a la Kelvin's and Clausius'. It suggests a modernized, combined statement: "A mesoscopic engine that works in completing irreversible internal cycles statistically has necessarily an external effect that lowering a weight accompanied by passing heat from a warmer to a colder body."

On Hardy-type integral inequalities in the whole plane related to the extended Hurwitz-zeta function

Using weight functions, we establish a few equivalent statements of two kinds of Hardy-type integral inequalities with nonhomogeneous kernel in the whole plane. The constant factors related to the extended Hurwitz-zeta function are proved to be the best possible. In the form of applications, we deduce some special cases involving homogeneous kernel. We additionally consider some particular inequalities and operator expressions.

On a reverse extended Hardy\u2013Hilbert\u2019s inequality

By the use of the weight coefficients, the idea of introducing parameters and the Euler–Maclaurin summation formula, a reverse extended Hardy–Hilbert inequality and the equivalent forms are given. The equivalent statements of the best possible constant factor related to a few parameters and some particular cases are also considered.

Quantum speed limits and the maximal rate of information production

The Bremermann-Bekenstein bound sets a fundamental upper limit on the rate with which information can be processed. However, the original treatment heavily relies on cosmological properties and plausibility arguments. In the present analysis, we derive equivalent statements by relying on only two fundamental results in quantum information theory and quantum dynamics -- Fannes inequality and the quantum speed limit. As main results, we obtain Bremermann-Bekenstein-type bounds for the rate of change of the von Neumann entropy in quantum systems undergoing open system dynamics, and for the rate of change of the Shannon information over some logical basis in unitary quantum evolution.

The Intersection Property of Annihilators of Both Modules and Maximal Submodules Belonging to the Same Module

During that article T stands for a commutative ring with identity and that S stands for a unitary module over T. The intersection property of annihilatoers of a module X on a ring T and a maximal submodule W of M has been reviewed under this article where he provide several examples that explain that the property. Add to this a number of equivalent statements about the intersection property have been demonstrated as well as the direct sum of module that realize that the characteristic has studied here we proved that the modules that achieve the intersection property are closed under the direct sum with a specific condition. In addition to all this, the relationship between the modules that achieve the above characteristics with other types of modules has been given.

Onpairwise Compactness in Fuzzy Finebi- Topological Spaces

In this paper the concepts of Pairwise ( , ) if jf T T fuzzy fine dually open cover, Pairwise ( , ) if jf T T fuzzy fine dually compact spacesand Pairwise ( , ) if jf T T fuzzy fine connected spaces are introduced and also an equivalent statement on Pairwise ( , ) if jf T T fuzzy fine dually compact spaces is established.