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Near ring is a generalization of ring: addition need not beabelian, and (more importantly) only one distributive law is postulated. In this paper, we establish a new generalization of near ring, na...

Eco-innovations are increasingly manufactured and consumed across national borders. Although global outsourcing can be financially profitable, it is questionable whether consumers respond to eco-innovations manufactured in different countries in the same way. This article introduces the ecological country-of-manufacture (COM) concept, which reflects consumers’ perception of a country’s commitment to sustainable development policy and practices. Drawing on schema theory, the current research examines how consumer reactions to “ecological (in)congruence”—when the sustainability reputation of a COM is a (mis)match with product eco-friendliness levels—vary across product categories (Study 1a), consumption contexts (Study 1b), and national settings (Study 2). Consumers report more preferential evaluations when there is ecological incongruence for privately consumed products and ecological congruence for publicly consumed products. The results also demonstrate the differential moderating effects of socioeconomic development factors and cultural dimensions. In emerging markets with highly embedded, hierarchical, and high-harmony cultures, consumers require ecological congruence to justify their adoption decisions, whereas in developed markets with highly autonomous, egalitarian, and high-mastery cultures, consumers are more likely to adopt eco-innovations that are ecologically incongruent.

In this paper, the concept of (strong) hyper equality ideals in bounded hyper equality algebras are introduced and several properties and related results are given. Also, the properties of hyper equality ideals of the direct product of bounded hyper equality algebras are investigated; we prove that any (strong) hyper equality ideal of the direct product of hyper equality algebras is representable with respect to the product of (strong) hyper equality ideals of any direct component. In the sequel, we investigate the relationships between hyper equality ideals and hyper deductive systems in good bounded hyper equality algebras. Furthermore, we show how one can construct a hyper congruence relation via a strong hyper equality ideal so that the congruence classes form a hyper equality algebra.

In this paper, we introduce the concept of fuzzy congruence relations on a pseudo BE-algebra and some of properties are investigated. We show that the set of all fuzzy congruence relations is a modular lattice and the quotient structure induced by fuzzy congruence relations is studied.

Let $$\mathbf{A}= (A_1, \ldots , A_m)$$ , where $$A_1, \ldots , A_m$$ are $$n\times n$$ real matrices. The real joint (p, q)-matricial range of $$\mathbf{A}$$ , $${\varLambda }^{{\mathbb {R}}}_{p,q}(\mathbf{A})$$ , is the set of m-tuple of $$q\times q$$ real matrices $$(B_1, \ldots , B_m)$$ such that $$(X^*A_1X, \ldots , X^*A_mX) = (I_p\otimes B_1, \ldots , I_p \otimes B_m)$$ for some real $$n \times pq$$ matrix X satisfying $$X^*X = I_{pq}$$ . It is shown that if n is sufficiently large, then the set $${\varLambda }^{{\mathbb {R}}}_{p,q}(\mathbf{A})$$ is non-empty and star-shaped. The result is extended to bounded linear operators acting on a real Hilbert space $${{{\mathcal {H}}}}$$ , and used to show that the joint essential (p, q)-matricial range of $$\mathbf{A}$$ is always compact, convex, and non-empty. Similar results for the joint congruence matricial ranges on complex operators are also obtained.

Since factor analysis is one of the most often used techniques in psychometrics, comparing or combining solutions from different factor analyses is often needed. Several measures to compare factors exist, one of the best known is Tucker's congruence coefficient, which is enjoying newly found popularity thanks to the recent work of Lorenzo-Seva and ten Berge (2006), who established cut-off values for factor congruence. While this coefficient is in most cases very good in comparing factors in general, it also has some disadvantages, which can cause trouble when one needs to compare or combine many analyses. In this paper, we propose a modified Tucker's congruence coefficient to address these issues. Lovik, A (corresponding author), Univ Leuven, I BioStat, KU Leuven, Kapucijnenvoer 35 Blok D, B-3000 Leuven, Belgium. aniko.lovik@kuleuven.be

A family of type N exact solution of the Einstein's field equations, regular everywhere except on the symmetry axis where it possesses a naked curvature singularity, is present. The stress-energy tensor is of the anisotropic fluid coupled with pure radiation field satisfy the different energy conditions and the physical parameters diverge $r \rightarrow 0$. The space-time admitting a non-expanding, non-twisting, and shear-free geodesic null congruence and belongs to a special class of type N Kundt metrics. The space-time is geodesically complete along the radiation direction in the constant $z$-planes and exhibits geometrically different properties from the known pp-waves. The present family of solution admits closed time-like curves (CTC) which appear after a certain instant of time and the space-time is a four-dimensional generalization of the Misner space metric in curved space-time., Comment: Typos corrected, accepted for publication in Gravitation and Cosmology

We use transference principle to show that whenever $s$ is suitably large depending on $k \geq 2$, every sufficiently large natural number $n$ satisfying some congruence conditions can be written in the form $n = p_1^k + \dots + p_s^k$, where $p_1, \dots, p_s \in [x-x^\theta, x + x^\theta]$ are primes, $x = (n/s)^{1/k}$ and $\theta = 0.525 + \epsilon$. We also improve known results for $\theta$ when $k \geq 2$ and $s \geq k^2 + k + 1$. For example when $k \geq 4$ and $s \geq k^2 + k + 1$ we have $\theta = 0.55 + \epsilon$. All previously known results on the problem had $\theta > 3/4$.

The ★ -congruence Sylvester equation is the matrix equation A X + X ⋆ B = C , where A ∈ F m × n , B ∈ F n × m and C ∈ F m × m are given, whereas X ∈ F n × m is to be determined. Here, F = R or C , ...

Let $f$ and $g$ be holomorphic cusp forms of weights $k_1$and $k_2$ for the congruence subgroups$\Gamma_0(~\mathcal{N}_1~)$ and $\Gamma_0(~\mathcal{N}_2~)$,respectively. In this paper the square moment of theRankin-Selberg $L$-function for $f$ and $g$ in the aspect of both weights in short intervals is bounded, when$k_1^\varepsilon\ll~k_2\ll~k_1^{1-\varepsilon}$.These bounds are the mean Lindelof hypothesis in one caseand subconvexity bounds on average in other cases. Thesesquare moment estimates also imply subconvexity bounds forindividual $L(\frac12+{\rm~i}t,f\times~g)$ for all $g$ when $f$is chosen outside a small exceptional set. In the bestcase scenario the subconvexity bound obtained reaches theWeyl-type bound proved by Lau et al. (2006) inboth the $k_1$ and $k_2$ aspects.

In this paper, we present the notions of α-ideal and α-congruence on a distributive nearlattice. We prove that the α-ideals and α-congruences of a normal distributive lattice A are in a one-to-one ...

We generalize several recognizability theorems for free single-sorted algebras to free many-sorted algebras and provide, in a uniform way and without using either regular tree grammars or tree automata, purely algebraic proofs of them based on congruences.

A method for constructing, using a computer, the envelope of a family of circles of variable radius, the centers of which are located on a given curve G and touch the circle C with the center at the origin, is given. In this case, the limits of the parameter t I [a, b], which determines the position of the center of each family circle on the curve G., are taken into account. In solving this problem, in the general case, the question arises of ordering the set of calculated coordinates of points on the corresponding branches of the envelope, which is difficult to formalize. In this paper, it is proposed to simplify the process of approximate finding of points on the envelope by calculating the coordinates of the points of intersection of "neighboring" pairs of circles. Namely, from N circles of the family SN, their pairs SK and SK+1 (K = 1..N-1) are sequentially selected, and common points are calculated for them. Then it can be argued that the set of found intersection points of all circles will be located on the branches of the desired envelope. О. Podgorny suggested using the above geometric model for interpretation at the graphic level of the relationship between the phases of the incident wave on the curve Г and the reflected wave from the curve G. Let the origin point be the source of the incident wave. Then the phase of the reflected wave from curve G can be considered orthotomics. The possibility of using orthotomics as lines for which the reflected rays constitute, respectively, a bundle or congruence of normals, О. Podgorny also demonstrated for the case of parallel incident rays. Here, as a basis for constructive constructions, mappings from a line in a plane were considered. The direct and orthotomics in the plane are the fronts of the incident and reflected waves, respectively, since the incident and reflected rays are their normals. The paper presents a computer implementation of the graphical method for determining the individual phases of the reflected waves, which correspond to the phases of the wave with a point source. These studies are important in solving problems in the field of architectural and construction physics and solar technology, which require the further development of constructive methods for modeling the reflected streams of sound or light.

Let $\overline{t}(n)$ be the number of overpartitions in which (i) the difference between successive parts may be odd only if the larger part is overlined and (ii) if the smallest part is odd then it is overlined. Ramanujan-type congruences for $\overline{t}(n)$ modulo small powers of $2$ and $3$ have been established. We present two infinite families of congruences modulo $5$ and $27$ for $\overline{t}(n)$, the first of which generalises a recent result of Chern and Hao [‘Congruences for two restricted overpartitions’, Proc. Math. Sci. 129 (2019), Article 31].

In this paper, a generalization of the Petersson trace formula for holomorphic parabolic forms with positive even weight with respect to congruence subgroup \Gamma_0 (N) of the Dirichlet character modulo N is proved

Some elements of tame congruence theory can be applied to quasiorder lattices instead of congruence lattices. In particular, it is possible to consider minimal sets of an algebra with respect to one of its prime quasiorder quotients. It turns out that if a finite algebra is in a congruence modular variety, then it is minimal with respect to a quasiorder quotient iff it is minimal with respect to a congruence quotient — in which case it is either a two-element algebra, or has a Mal’tsev-polynomial. As an application of this fact, we prove that if an algebra is in a congruence modular variety, its congruence and quasiorder lattices satisfy the same identities.

Let p be an odd prime, the harmonic congruence such as , and many different variations and generalizations have been studied intensively. In this note, we consider the congruences involving the combination of alternating harmonic sums, where PP denotes the set of positive integers which are prime to p. And we establish the combinational congruences involving alternating harmonic sums for positive integer n=3,4,5.

In this paper, we use elementary methods, properties of Gauss sums and estimates for character sums to study a problem related to primitive roots, and prove the following result. Let $p$ be a large enough odd prime. Then for any two distinct integers $a, b \in \{1, 2, \cdots, p-1\}$, there exist three primitive roots $\alpha$, $\beta$ and $\gamma$ modulo $p$ such that the congruence equations $\alpha+\gamma\equiv a\bmod p$ and $\beta+\gamma\equiv b\bmod p$ hold.

Let \begin{document}$ n $\end{document} be a nonnegative integer. The \begin{document}$ n $\end{document} -th Apery number is defined by \begin{document}$ A_n: = \sum\limits_{k = 0}^n\binom{n+k}{k}^2\binom{n}{k}^2. $\end{document} Z.-W. Sun investigated the congruence properties of Apery numbers and posed some conjectures. For example, Sun conjectured that for any prime \begin{document}$ p\geq7 $\end{document} \begin{document}$ \sum\limits_{k = 0}^{p-1}(2k+1)A_k\equiv p-\frac{7}{2}p^2H_{p-1}\pmod{p^6} $\end{document} and for any prime \begin{document}$ p\geq5 $\end{document} \begin{document}$ \sum\limits_{k = 0}^{p-1}(2k+1)^3A_k\equiv p^3+4p^4H_{p-1}+\frac{6}{5}p^8B_{p-5}\pmod{p^9}, $\end{document} where \begin{document}$ H_n = \sum_{k = 1}^n1/k $\end{document} denotes the \begin{document}$ n $\end{document} -th harmonic number and \begin{document}$ B_0, B_1, \ldots $\end{document} are the well-known Bernoulli numbers. In this paper we shall confirm these two conjectures.

This article investigated the idea of Shape of numbers and introduced new operators. The idea divides all products of k distinct integers in [1, n - 1] into 2K-1 catalogs and derives the calculation formula of every catalog. As a simple deduction, a direct formula of the Stirling numbers of the first kind S1(n, n - k) and a simple recursive formula of Stirling numbers of the second kind S2(n, n - k) are obtained. By analyzing the Shape of numbers, new congruence formulas are obtained.

For each positive integer $n$, let $g_\Delta(n)$ be the smallest positive integer $g$ such that every complete quadratic polynomial in $n$ variables which can be represented by a sum of odd squares is represented by a sum of at most $g$ odd squares. In this paper, we analyze $g_\Delta(n)$ by studying representations of integral quadratic forms by sums of squares with certain congruence condition. We prove that the growth of $g_\Delta(n)$ is at most an exponential of $\sqrt{n}$, which is the same as the best known upper bound on the $g$-invariants of the original quadratic Waring's problem. We also determine the exact value of $g_\Delta(n)$ for each positive integer less than or equal to $4$., Comment: 22 pages

We establish transformation laws for generalized Dedekind sums associated to the Kronecker limit function of non-holomorphic Eisenstein series and their higher-order variants. These results apply to general Fuchsian groups of the first kind, and examples are provided in the cases of the Hecke triangle groups, the Hecke congruence groups $\Gamma_0(N)$, and the non-congruence arithmetic groups $\Gamma_0(N)^+$., Comment: 18 pages

Health appeals to promote wellness and healthful choices can be framed individually or socially (benefit to self/others). Across three studies, the authors identify the influence of self-construal ...

Given a prime p, an integer $$H\in [1,p)$$, and an arbitrary set $${\mathcal {M}} \subseteq {\mathbb {F}} _p^*$$, where $${\mathbb {F}} _p$$ is the finite field with p elements, let $$J(H,{\mathcal {M}} )$$ denote the number of solutions to the congruence $$\begin{aligned} xm\equiv yn~\mathrm{mod}~ p \end{aligned}$$for which $$x,y\in [1,H]$$ and $$m,n\in {\mathcal {M}} $$. In this paper, we bound $$J(H,{\mathcal {M}} )$$ in terms of p, H, and the cardinality of $${\mathcal {M}} $$. In a wide range of parameters, this bound is optimal. We give two applications of this bound: to new estimates of trilinear character sums and to bilinear sums with Kloosterman sums, complementing some recent results of Kowalski et al. (Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums, 2018, arXiv:1802.09849).

In this paper, we consider the congruence equation [Formula: see text] with [Formula: see text] where [Formula: see text] denotes the multiplicative inverse of [Formula: see text]. We prove that its number of solutions is asymptotic to [Formula: see text] when [Formula: see text] by estimating a certain average of Kloosterman sums via Gauss sums. On the other hand, when [Formula: see text], the number of solutions has order of magnitude at least [Formula: see text]. It would be interesting to better understand its transition of behavior. By transforming the question slightly, one can relate the problem to a certain first moment of Dirichlet [Formula: see text]-functions at [Formula: see text].

Let F n be the free group on n generators. Consider the group I A n of automorphisms of F n acting trivially on its abelianization . There are two canonical filtrations on I A n : the first one is its lower central series Γ ⁎ ; the second one is the Andreadakis filtration A ⁎ , defined from the action on F n . In this paper, we establish that the canonical morphism between the associated graded Lie rings L ( Γ ⁎ ) and L ( A ⁎ ) is stably surjective. We then investigate a p -restricted version of the Andreadakis problem. A calculation of the Lie algebra of the classical congruence group is also included.

Nielsen reports Black buying power is expected to increase to nearly $2 trillion by 2021. Thus our research is rooted in offering intellectual support to exploring that economic contribution and fi...

We investigate the arithmetic properties of the second-order mock theta function $B(q)$ and establish two identities for the coefficients of this function along arithmetic progressions. As applications, we prove several congruences for these coefficients.

In the vocation of nutrition science, tremendous research has been executed over the analysis of food, its chemistry, conservation, preparation, consumption, production, deficiencies and so on. Even in present time professionals have pinned their eye over the manner of intake of food too, but the water being very essential element for survival has not been yet attracted the attention of the heavenly body. Ayurveda, one of the most ancient traditional systems of medicine contemplated water as an endorser of life which plays a pivot role in attaining vigor or occurrence of maladies. The scriptures divulged the facts that proper nourishment and metabolism of body also rely on the quality, quantity and even on the right manner of intake of water along with other major nutrients, and regarding this, a very comprehensive narrative is found in all the obtainable treatises of ancient medical science. This inspires the researcher to highlight such codes which can be directed as an additive protocol for the human being having pursuance of health. Moreover, an extensive search has also been performed to find out the parallel scientific evidences regarding the dogmas which can be established over the scientific background, so to make it more acceptable and admissible in the community and to also provide a pointer on which further research could be carried out.

An n-by-n real symmetric matrix is called copositive if its quadratic form is nonnegative on nonnegative vectors. Our interest is in identifying which linear transformations on symmetric matrices preserve copositivity either in the into or onto sense. We conjecture that in the onto case, the map must be congruence by a monomial matrix (a permutation times a positive diagonal matrix). This is proven under each of some additional natural hypotheses. Also, the into preservers of standard type are characterized. A general characterization in the into case seems di¢ cult, and examples are given. One of them provides a counterexample to a conjecture about the into preservers., This work was partially supported by project UID/MAT/04721/2019 and by project UID/MAT/00013/2013

In this paper, we mainly prove a congruence conjecture of M. Apagodu [3] and a supercongruence conjecture of Z.-W. Sun [25] .

Let [Formula: see text] be a positive odd integer and [Formula: see text] a positive integer with [Formula: see text]. We prove that [Formula: see text] Here [Formula: see text], [Formula: see text] denotes the Jacobi symbol, and [Formula: see text] is the [Formula: see text]th cyclotomic polynomial in [Formula: see text]. This confirms a recent conjecture of the first author.

We consider the canonical basis elements f k , m e for the space of weakly holomorphic modular forms of weight k for the Hecke congruence group Γ 0 ( 2 ) and we prove that for all m ≥ c ( k ) for some constant c ( k ) , if z 0 in a fundamental domain for Γ 0 ( 2 ) is a zero of f k , m e , then either z 0 is in { i 2 , − 1 2 + i 2 , 1 2 + i 2 , − 1 + i 7 4 , 1 + i 7 4 } , or z 0 is transcendental.

We discussq-analogues of the classical congruence$$\left( {\begin{array}{c}ap\\ bp\end{array}}\right) \equiv \left( {\begin{array}{c}a\\ b\end{array}}\right) \pmod {p^3}$$apbp≡ab(modp3), for primes$$p>3$$p>3, as well as its generalisations. In particular, we prove related congruences for (q-analogues of) integral factorial ratios.

We characterize those algebras that have infinitely many polynomially inequivalent expansions among all finite nilpotent algebras of finite type in congruence modular varieties that are direct products of algebras of prime power order.

This study attempts to assess the influence of investor-advisor personality congruence on the trading behavior of futures investor. This research tested the hypotheses based on the unique d...

Recent discussions of the epistemological and political implications of the situatedness of knowledge in International Relations (IR) have raised important questions regarding the future development of the discipline. They pose the challenge of understanding under what conditions human beings develop more or less reality-congruent knowledge about world politics and what are the implications of such knowledge for emancipatory political activity. This article argues that process sociology should be understood as a relevant complement to these discussions. Assuming a fundamentally ‘realist’ orientation, process sociology provides a sociologically informed analysis of the material, ideational and emotional forces shaping the development of knowledge. As such, it can help those concerned with the implications of the situatedness of knowledge in IR reinforce their capacity to both understand the social conditions under which it is possible to develop more detached and reality-congruent knowledge about the world and better identify and explain the historically emergent values that should orientate the emancipatory transformation of world politics.

This study aimed to examine whether budget goal commitment, psychological capital, and management accounting system were able to play a role in mediating the relation between budget congruence and managerial performance in public services universities in Indonesia. This study used a quantitative survey approach; the sample of the study consisted of 82 leaders from State Islamic Universities in the province of East Java, Indonesia. The data were analyzed by using a causal mediation analysis procedure. The result found that psychological capital and management accounting systems were able to mediate the budget congruence-managerial performance relation. Meanwhile, budget goal commitment in the context of public sector budgeting has not succeeded in proving its role as a mediating variable. Further analysis showed that contingency theory is still relevant to be used in business and public budgeting in relation to different behavioural conditions. In addition, this research has implications for evaluating the managerial performance of leaders in public services universities in Indonesia to pay attention on managerial involvement at lower levels in achieving organizational goals.

CAMO provides a rigorous and user-friendly solution for quantification and mechanistic exploration of omics congruence in model organisms and humans. It performs threshold-free differential analysis, quantitative concordance/discordance scoring, pathway-centric investigation, and topological subnetwork detection. Instead of dichotomous claims of “poorly” or “greatly” mimicking humans, CAMO facilitates discovery and visualization of specific molecular mechanisms that are best or least mimicked, providing foundations for hypothesis generation and subsequent translational investigations.

Tunneling magnetoresistive (TMR) sensors have broad application prospects because of their high sensitivity and small volume. However, the inherent hysteresis characteristics of TMR affect its applications in high accuracy scenarios. It is essential to build a model to describe the attributes of hysteresis of TMR accurately. Preisach model is one of the popular models to describe the behavior of inherent hysteresis for TMR, whereas it presents low accuracy in high-order hysteresis reversal curves. Furthermore, the traditional Preisach model has strict congruence constraints, and the amount of data seriously affects the accuracy. This paper proposes a hysteresis model from a probability perspective. This model has the same computational complexity as the classic Preisach model while presenting higher accuracy, especially in high-order hysteresis reversal curves. When measuring a small amount of data, the error of this method is significantly reduced compared with the classical Preisach model. Besides, the proposed model’s congruence in this paper only needs equal vertical chords.