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In this paper we complement and generalize some constructions of fuzzy implications based on two arbitrary copulas, obtaining new fuzzy implications. By means of (restricted) aggregation functions acting on [ 0 , 1 ] S , where S is a fixed finite or infinite set, and related S -systems of fuzzy implications and transforming functions, we introduce and discuss a rather general method for constructing fuzzy implications. Several examples illustrating our results are also included. [ABSTRACT FROM AUTHOR]

In this work, h w -lifting modules, a special extension of h -lifting which is a further generalization of lifting modules, are studied. Here, we observed that finite direct sum of h w -lifting modules may not be h w -lifting, so we provided various sufficient conditions for which h w -lifting modules are closed under direct sum. Moreover, we have introduced and studied the properties of a new version of h -lifting module namely, m h -lifting, m h w -lifting and completely m h -lifting modules and develop some more properties of the h w -lifting modules in terms of these modules. Further, we proved that if the direct sum of arbitrary family of hollow modules is m h -lifting, then the arbitrary direct sum of m h -lifting R -module is again m h -lifting. [ABSTRACT FROM AUTHOR]

We study a certain class of piecewise monotonic maps of an interval. These maps are strictly monotone on finite interval partitions, satisfy the Markov condition, and have generator property. We show that for a function from this class distributional chaos is always present and we study its basic properties. The main result states that the distributional spectrum, as well as the weak spectrum, is always finite. This is a generalization of a similar result for continuous maps on the interval, circle, and tree. An example is given showing that conditions on the mentioned class can not be weakened. [ABSTRACT FROM AUTHOR]

Twisted knot theory, introduced by Bourgoin, is a generalization of virtual knot theory. It is well known that any virtual knot can be deformed into a trivial knot by a finite sequence of generalized Reidemeister moves and two forbidden moves F 1 and F 2. Similarly, we show that any twisted knot also can be deformed into a trivial knot or a trivial knot with a bar by a finite sequence of extended Reidemeister moves and three forbidden moves T 4 , F 1 (or F 2) and F 3 (or F 4). [ABSTRACT FROM AUTHOR]

The investigation of orthodox P -restriction semigroups was initiated by Jones in 2014 as generalizations of orthodox * -semigroups. The aim of this paper is to further study orthodox P -restriction semigroups based on the known results of Jones. After establishing a construction theorem for orthodox P -restriction semigroups, we introduce proper P -restriction semigroups (which are necessarily orthodox) and prove that every (finite) orthodox P -restriction semigroup has a (finite) proper cover. Our results enrich and extend existing results for restriction semigroups and orthodox * -semigroups. [ABSTRACT FROM AUTHOR]

We formulate a general problem: Given projective schemes Y$\mathbb {Y}$ and X$\mathbb {X}$ over a global field K and a K‐morphism η from Y$\mathbb {Y}$ to X$\mathbb {X}$ of finite degree, how many points in X(K)$\mathbb {X}(K)$ of height at most B have a pre‐image under η in Y(K)$\mathbb {Y}(K)$? This problem is inspired by a well‐known conjecture of Serre on quantitative upper bounds for the number of points of bounded height on an irreducible projective variety defined over a number field. We give a nontrivial answer to the general problem when K=Fq(T)$K=\mathbb {F}_q(T)$ and Y$\mathbb {Y}$ is a prime degree cyclic cover of X=PKn$\mathbb {X}=\mathbb {P}_{K}^n$. Our tool is a new geometric sieve, which generalizes the polynomial sieve to a geometric setting over global function fields. [ABSTRACT FROM AUTHOR]

The Jacobian algebra arising from a consistent dimer model is a bimodule 3-Calabi–Yau algebra, and its center is a 3-dimensional Gorenstein toric singularity. A perfect matching (PM) of a dimer model gives the degree, making the Jacobian algebra |$\mathbb{Z}$| -graded. It is known that if the degree zero part of such an algebra is finite dimensional, then it is a 2-representation infinite algebra that is a generalization of a representation infinite hereditary algebra. Internal PMs, which correspond to toric exceptional divisors on a crepant resolution of a 3-dimensional Gorenstein toric singularity, characterize the property that the degree zero part of the Jacobian algebra is finite dimensional. Combining this characterization with the theorems due to Amiot–Iyama–Reiten, we show that the stable category of graded maximal Cohen–Macaulay modules admits a tilting object for any 3-dimensional Gorenstein toric isolated singularity. We then show that all internal PMs corresponding to the same toric exceptional divisor are transformed into each other using the mutations of PMs, and this induces derived equivalences of 2-representation infinite algebras. [ABSTRACT FROM AUTHOR]

We introduce an idea of closed weak Rad-supplemented module (briefly, cwrs) as a proper generalization of both extending and weak Rad-supplemented (briefly, wrs) modules, by weakening the extending condition that is closed submodule is a direct summand by the closed submodule has a wrs. It observed that cwrs module is not inherited by direct sum and homomorphic image, examples are provided in Remark 2.6 and Remark 2.16. In this regard we proved several results under some conditions which showed that cwrs is closed under finite direct sum and homomorphic image. Couple of them are listed as: i) A local distributive (or duo or distributive) module M = M1 ⊕ M2 is cwrs if and only if each components M1 and M2 are cwrs. ii) Every non-singular homomorphic image of a cwrs module is again a cwrs. [ABSTRACT FROM AUTHOR]

We consider conformal homeomorphisms \varphi of generalized Jordan domains U onto planar domains \Omega that satisfy both of the next two conditions: (1) at most countably many boundary components of \Omega are non-degenerate and their diameters have a finite sum; (2) either the degenerate boundary components of \Omega or those of U form a set of sigma-finite linear measure. We prove that \varphi continuously extends to the closure of U if and only if every boundary component of \Omega is locally connected. This generalizes the Carathéodory's Continuity Theorem and leads us to a new generalization of the well known Osgood-Taylor-Carathéodory Theorem. There are three issues that are noteworthy. Firstly, none of the above conditions (1) and (2) can be removed. Secondly, our results remain valid for non-cofat domains and do not follow from the extension results, of a similar nature, that are obtained in very recent studies on the conformal rigidity of circle domains. Finally, when \varphi does extend continuously to the closure of U, the boundary of \Omega is a Peano compactum. Therefore, we also show that the following properties are equivalent for any planar domain \Omega: [ABSTRACT FROM AUTHOR]

Given a non-empty set X and let P(X) be a partial transformation semigroup on X. For a fixed subset Y of X, define a generalization of P(X) by PFix (X , Y) = { α ∈ P (X) : y α = y for all y ∈ dom (α) ∩ Y }. In this article, we give a complete description of Green's relations on PFix(X, Y) and apply this to obtain the characterizations of left regular, right regular, intra-regular and completely regular elements of PFix(X, Y). The number and the relationship between these elements are also investigated by using finiteness of X and X ∖ Y. [ABSTRACT FROM AUTHOR]

The concept of the direct product of finite family of B-algebras is introduced by Lingcong and Endam[J. A. V. Lingcong and J. C. Endam, Direct product of B-algebras, Int. J. Algebra, 10(1):33-40, 2016.]. In this paper, we introduce the concept of the direct product of infinite family of B-algebras, we call the external direct product, which is a generalization of the direct product in the sense of Lingcong and Endam. Also, we introduce the concept of the weak direct product of B-algebras. Finally, we provide several fundamental theorems of (anti-)B-homomorphisms in view of the external direct product B-algebras. [ABSTRACT FROM AUTHOR]

Leighton's graph covering theorem says that two finite graphs with a common cover have a common finite cover. We present a new proof of this using groupoids, and use this as a model to prove two generalisations of the theorem. The first generalisation, which we refer to as the symmetry-restricted version, restricts how balls of a given size in the universal cover can map down to the two finite graphs when factoring through the common finite cover - this answers a question of Neumann (2010). Secondly, we consider covers of graphs of spaces (or of more general objects), which leads to an even more general version of Leighton's theorem. We also compute upper bounds for the sizes of the finite covers obtained in Leighton's theorem and its generalisations. An appendix by Gardam and Woodhouse provides an alternative proof of the symmetry-restricted version, that uses Haar measure instead of groupoids. [ABSTRACT FROM AUTHOR]

Let X / s be a proper log smooth scheme of Cartier type over a fine log scheme whose underlying scheme is the spectrum of a perfect field κ of characteristic p > 0 . In this article we prove that the cohomology of 풲 ⁢ (풪 X) is a finitely generated 풲 ⁢ (κ) -module if the Yobuko height of X is finite. As an application of this result, we prove that, if the Yobuko height of a proper smooth threefold Y over κ is finite, then the crystalline cohomology of Y / κ has the Hodge–Witt decomposition and the p-primary torsion part of the Chow group of codimension 2 of Y is of finite cotype. These are nontrivial generalizations of results in [K. Joshi and C. S. Rajan, Frobenius splitting and ordinarity, Int. Math. Res. Not. IMRN 2003 2003, 2, 109–121] and [K. Joshi, Exotic torsion, Frobenius splitting and the slope spectral sequence, Canad. Math. Bull. 50 2007, 4, 567–578]. We also prove a fundamental inequality between the Artin–Mazur heights and the Yobuko height of X / s if X / s satisfies natural conditions. [ABSTRACT FROM AUTHOR]

Dibands and tribands are generalizations of bands. Zhuchok asked two open problems on constructing a free diband in 2017 and on constructing a free triband in 2019. We solve these two open problems and calculate the cardinality of the free diband (resp. free triband) generated by an arbitrary finite set. Moreover, we prove that the word problem for free dibands (resp. free tribands) is solvable. [ABSTRACT FROM AUTHOR]

We present a family of new M2-brane solutions in AdS7× S4 that calculate toroidal BPS surface operators in the N = (2, 0) theory. These observables are conformally invariant and not subject to anomalies so we are able to evaluate their finite expectation values at leading order at large N. In the limit of a thin torus we find a cylinder, which is a natural surface generalization of both the circular and parallel lines Wilson loop. We study and comment on this limit in some detail. [ABSTRACT FROM AUTHOR]

Let R be a regular ring, let J be an ideal generated by a regular sequence of codimension at least 2, and let I be an ideal containing J. We give an example of a module H I 3 (J) with infinitely many associated primes, answering a question of Hochster and Núñez-Betancourt in the negative. In fact, for i ≤ 4 , we show that under suitable hypotheses on R / J , Ass H I i (J) is finite if and only if Ass H I i − 1 (R / J) is finite. Our proof of this statement involves a novel generalization of an isomorphism of Hellus, which may be of some independent interest. The finiteness comparison between Ass H I i (J) and Ass H I i − 1 (R / J) tends to improve as our hypotheses on R / J become more restrictive. To illustrate the extreme end of this phenomenon, at least in the prime characteristic p > 0 setting, we show that if R / J is regular, then Ass H I i (J) is finite for all i ≥ 0. [ABSTRACT FROM AUTHOR]

For a PV thread T which accesses a set R of resources, each with a maximal capacity κ : R → N , the PV-program T n , where n copies of T are run in parallel, is deadlock free for all n if and only if T M is deadlock free where M is the sum of the capacities of the shared resources M = Σ r ∈ R κ (r) . This is a sharp bound: For all κ : R → N and finite R there is a thread T using these resources such that T M has a deadlock, but T n does not for n < M . Moreover, we prove a more general theorem for a set of different threads sharing resources R : There are no deadlocks in p = T 1 | T 2 | ⋯ | T n if and only if there are no deadlocks in T i 1 | T i 2 | ⋯ | T i M for any M-element subset { i 1 , ... , i M } ⊂ [ 1 : n ] . For κ (r) ≡ 1 , T n is serializable, i.e., all executions are equivalent to serial executions, for all n if and only if T 2 is serializable. For general capacities, we define local obstructions to serializability—if no such obstruction exists, the program is serializable. There is no local obstruction to serializability in T n for all n if and only if there is no local obstruction to serializability in T M for M = Σ r ∈ R κ (r) + 1 . The obstructions may be found using a deadlock algorithm in T M + 1 . There is a generalization to p = T 1 | T 2 | ⋯ | T n : If there are no local obstructions to serializability in any of the sub programs, T i 1 | T i 2 | ⋯ | T i M , then p is serializable. [ABSTRACT FROM AUTHOR]

We extend the classical notion of standardly stratified k-algebra (stated for finite dimensional k-algebras) to the more general class of rings, possibly without 1, with enough idempotents. We show that many of the fundamental results, which are known for classical standardly stratified algebras, can be generalized to this context. Furthermore, new classes of rings appear as: ideally standardly stratified and ideally quasi-hereditary. In the classical theory, it is known that quasi-hereditary and ideally quasi-hereditary algebras are equivalent notions, but in our general setting, this is no longer true. To develop the theory, we use the well-known connection between rings with enough idempotents and skeletally small categories (ringoids or rings with several objects). [ABSTRACT FROM AUTHOR]

A purely inseparable field extension K of a field k of characteristic p 6= 0 is said to be !0-generated over k if K=k is not finitely generated, but L=k is finitely generated for each proper intermediate field L. In 1986, Deveney solved the question posed by R. Gilmer and W. Heinzer, which consists in knowing if the lattice of intermediate fields of an !0-generated field extension K=k is necessarily linearly ordered under inclusion, by constructing an example of an !0-generated field extension where [kp-n \ K: k] = p2n for all positive integer n. This example has proved to be extremely useful in the construction of other examples of !0-generated field extensions (of any finite irrationality degree). In this paper, we characterize the extensions of finite irrationality degree which are !0-generated. In particular, in the case of unbounded irrationality degree, any modular extension of unbounded exponent contains a proper subfield of unbounded exponent over the ground field. Finally, we give a generalization, illustrated by an example, of the !0-generated to include modular purely inseparable extensions of unbounded irrationality degree. [ABSTRACT FROM AUTHOR]

As a common generalization of Rickart -rings and generalized Baer -rings, we say that a ring with an involution is a generalized Rickart -ring if for all the right annihilator of is generated by a projection for some positive integer depending on . The abelian generalized Rickart -rings are closed under finite direct product. We address the behavior of the generalized Rickart condition with respect to various constructions and extensions, present some families of generalized Rickart -rings, study connections to the related classes of rings, and indicate various examples of generalized Rickart -rings. Also, we provide some large classes of finite and infinite-dimensional Banach -algebras that are generalized Rickart -rings but neither Rickart -rings nor generalized Baer -rings. [ABSTRACT FROM AUTHOR]

A rooted digraph is a vertex-flame if for every vertex v there is a set of internally disjoint directed paths from the root to v whose set of terminal edges covers all ingoing edges of v. It was shown by Lovász that every finite rooted digraph admits a spanning subdigraph which is a vertex-flame and large, where the latter means that it preserves the local connectivity to each vertex from the root. Calvillo-Vives rediscovered and extended this theorem proving that every vertex-flame of a given finite rooted digraph can be extended to be large. The analogue of Lovász' result for countable digraphs was shown by the third author where the notion of largeness is interpreted in a structural way as in the infinite version of Menger's theorem. We give a common generalisation of this and Calvillo-Vives' result by showing that in every countable rooted digraph each vertex-flame can be extended to a large vertex-flame. [ABSTRACT FROM AUTHOR]

This paper investigates circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. We characterise the images of the curvature maps and establish several equivalent conditions regarding long time behaviors of Chow-Luo's combinatorial Ricci flows for these patterns. As consequences, several generalizations of circle pattern theorem are obtained. Moreover, our approach suggests a computational method to find the desired circle patterns. [ABSTRACT FROM AUTHOR]

Let $k$ be a perfect field of characteristic $p> 2$ , and let $K$ be a finite totally ramified extension of $W(k)\big[\frac{1}{p}\big]$ of ramification degree $e$. We consider an unramified base ring $R_0$ over $W(k)$ satisfying certain conditions, and let $R = R_0\otimes _{W(k)}\mathcal{O}_K$. Examples of such $R$ include $R = \mathcal{O}_K[\![s_1, \ldots , s_d]\!]$ and $R = \mathcal{O}_K\langle t_1^{\pm 1}, \ldots , t_d^{\pm 1}\rangle $. We show that the generalization of Raynaud's theorem on extending $p$ -divisible groups holds over the base ring $R$ when $e < p-1$ , whereas it does not hold when $R = \mathcal{O}_K[\![s]\!]$ with $e \geq p$. As an application, we prove that if $R$ has Krull dimension $2$ and $e < p-1$ , then the locus of Barsotti–Tate representations of $\textrm{Gal}(\overline{R}\big[\frac{1}{p}\big]/R\big[\frac{1}{p}\big])$ cuts out a closed subscheme of the universal deformation scheme. If $R = \mathcal{O}_K[\![s]\!]$ with $e \geq p$ , we prove that such a locus is not $p$ -adically closed. [ABSTRACT FROM AUTHOR]

We give examples of pseudoconvex domains of finite type in C2 where the Kohn algorithm for subelliptic estimates fails to yield an effective lower bound for the order of subellipticity in terms of the type. We show how to modify the algorithm to obtain an effective procedure to prove subellipticity on domains of finite type in C2 with real analytic boundary satisfying a condition slightly stronger than pseudoconvexity. We close with a generalization to higher dimensions. [ABSTRACT FROM AUTHOR]

The category of internal coalgebras in a cocomplete category with respect to a variety is equivalent to the category of left adjoint functors from to . This can be seen best when considering such coalgebras as finite coproduct preserving functors from o p , the dual of the Lawvere theory of , into : coalgebras are restrictions of left adjoints and any such left adjoint is the left Kan extension of a coalgebra along the embedding of o p into A l g . Since S Mod -coalgebras in the variety R Mod for rings R and S are nothing but left S -, right R -bimodules, the equivalence above generalizes the Eilenberg–Watts theorem and all its previous generalizations. By generalizing and strengthening Bergman's completeness result for categories of internal coalgebras in varieties, we also prove that the category of coalgebras in a locally presentable category is locally presentable and comonadic over and, hence, complete in particular. We show, moreover, that Freyd's canonical constructions of internal coalgebras in a variety define left adjoint functors. Special instances of the respective right adjoints appear in various algebraic contexts and, in the case where is a commutative variety, are coreflectors from the category C o a l g (,) into . [ABSTRACT FROM AUTHOR]

We give examples of pseudoconvex domains of finite type in C2 where the Kohn algorithm for subelliptic estimates fails to yield an effective lower bound for the order of subellipticity in terms of the type. We show how to modify the algorithm to obtain an effective procedure to prove subellipticity on domains of finite type in C2 with real analytic boundary satisfying a condition slightly stronger than pseudoconvexity. We close with a generalization to higher dimensions. [ABSTRACT FROM AUTHOR]

In this paper, we study a relationship between tilting modules with finite projective dimension and dominant dimension with respect to injective modules as a generalization of results of Crawley-Boevey–Sauter, Nguyen–Reiten–Todorov–Zhu and Pressland–Sauter. Moreover, we give characterizations of almost n -Auslander–Gorenstein algebras and almost n -Auslander algebras by the existence of tilting modules. As an application, we describe a sufficient condition for almost 1-Auslander algebras to be strongly quasi-hereditary by comparing such tilting modules and characteristic tilting modules. [ABSTRACT FROM AUTHOR]

We present a generalization of concept of bounded l-index for meromorphic functions of finite order. Using known results for entire functions of bounded l-index we obtain similar propositions for meromorphic functions. There are presented analogs of Hayman's theorem and logarithmic criterion for this class. The propositions are widely used to investigate l-index boundedness of entire solutions of differential equations. Taking this into account we raise a general problem of generalization of some results from theory of entire functions of bounded l-index by meromorphic functions of finite order and their applications to meromorphic solutions of differential equations. There are deduced sufficient conditions providing l-index boundedness of meromoprhic solutions of finite order for the Riccati differential equation. Also we proved that the Weierstrass ℘-function has bounded l-index with l(z) = |z| [ABSTRACT FROM AUTHOR]

We establish the uniform convergence of the control polygons generated by repeated degree elevation of q -Bézier curves (i.e. , polynomial curves represented in the q -Bernstein bases of increasing degrees) on [ 0 , 1 ] , q > 1 , to a piecewise linear curve with vertices on the original curve. A similar result is proved for q < 1 , but surprisingly the limit vertices are not on the original curve, but on the q − 1 -Bézier curve with control polygon taken in the reverse order. We introduce a q -deformation (quantum Lorentz degree) of the classical notion of Lorentz degree for polynomials and we study its properties. As an application of our convergence results, we introduce a notion of q -positivity which guarantees that the q -Lorentz degree is finite. We also obtain upper bounds for the quantum Lorentz degrees. Finally, as a by-product we provide a generalization to polynomials positive on q -lattices of the univariate Pólya theorem concerning polynomials positive on the non-negative axis. [ABSTRACT FROM AUTHOR]

In 2016, Garner and Schäppi gave a criterion for existence of finite biproducts in a specific class of monoidal categories. We provide an elementary proof of (a slight generalization of) their result. Also, we explain how to prove, by using the same technique, an analogous result including infinite biproducts. [ABSTRACT FROM AUTHOR]

This paper has triple main objectives. The first objective is an analysis of some auxiliary results on closedness and boundedness of linear relations. The second objective is to provide some new characterization results on semiclosed linear relations. Here it is shown that the class of semiclosed linear relations is invariant under finite and countable sums, products, and limits. We have obtained fundamental new results as well as a Kato Rellich Theorem for semiclosed linear relations and essentially interesting generalizations. The last objective deals with semiclosed linear relation with closed range, where we have particularly established new characterizations of closable linear relation. [ABSTRACT FROM AUTHOR]

It has been known for a long time that every finite orthodox completely regular semigroup has a finite basis of identities, and that every finite central completely simple semigroup has a finite basis of identities. In the present paper, a common generalization of these two facts is established. It is shown that every finite central locally orthodox completely regular semigroup has a finite basis of identities. The proof of this latter fact which is presented in this paper employs significantly the celebrated theorem of Libor Polák on the structure of the lattice of all varieties of completely regular semigroups. [ABSTRACT FROM AUTHOR]

The notion of weakly injective -act can be regarded as a generalization of the notion of injective -act. This article describes the finite monoids over which each weakly injective -act has a primitively normal theory. Moreover, we show that the primitive normality of the class of all principally weakly injective -acts is equivalent to being totally ordered. [ABSTRACT FROM AUTHOR]

This paper proposes two consistent model selection procedures for factor-augmented regressions (FAR) in finite samples. We first demonstrate that the usual cross-validation is inconsistent, but that a generalization, leave-d-out cross-validation, is consistent. The second proposed criterion is a generalization of the bootstrap approximation of the squared error of prediction to FARs. The paper provides the validity results and documents their finite sample performance through simulations. An illustrative empirical application that analyzes the relationship between the equity premium and factors extracted from a large panel of U.S. macroeconomic data is conducted. [ABSTRACT FROM AUTHOR]

In this paper, we establish a finiteness theorem for L p harmonic 1-forms on a locally conformally flat Riemannian manifold under the assumptions on the Schrödinger operators involving the squared norm of the traceless Ricci form. This result can be regarded as a generalization of Han's result on L 2 harmonic 1-forms. [ABSTRACT FROM AUTHOR]

Ihara et al. proved the derivation relation for multiple zeta values. The first-named author obtained its counterpart for finite multiple zeta values in ${\mathcal{A}}$. In this paper, we present its generalization in  $\widehat{{\mathcal{A}}}$. [ABSTRACT FROM AUTHOR]

We introduce irregular constructible sheaves, which are ${\mathbb {C}}$ -constructible with coefficients in a finite version of the Novikov ring $\Lambda$ and special gradings. We show that the bounded derived category of cohomologically irregular constructible complexes is equivalent to the bounded derived category of holonomic ${\mathcal {D}}$ -modules by a modification of D'Agnolo and Kashiwara's irregular Riemann–Hilbert correspondence. The bounded derived category of cohomologically irregular constructible complexes is equipped with the irregular perverse $t$ -structure, which is a straightforward generalization of usual perverse $t$ -structure, and we prove that its heart is equivalent to the abelian category of holonomic ${\mathcal {D}}$ -modules. We also develop the algebraic version of the theory. [ABSTRACT FROM AUTHOR]

A Noetherian (Artinian) Lie algebra satisfies the maximal (minimal) condition for ideals. Generalisations include quasi-Noetherian and quasi-Artinian Lie algebras. We study conditions on prime ideals relating these properties. We prove that the radical of any ideal of a quasi-Artinian Lie algebra is the intersection of finitely many prime ideals, and an ideally finite Lie algebra is quasi-Noetherian if and only if it is quasi-Artinian. Both properties are equivalent to soluble-by-finite. We also prove a structure theorem for serially finite Artinian Lie algebras. [ABSTRACT FROM AUTHOR]

The O'Hara energies, introduced by Jun O'Hara in 1991, were proposed to answer the question of what is a "good" figure in a given knot class. A property of the O'Hara energies is that the "better" the figure of a knot is, the less the energy value is. In this article, we discuss two topics on the O'Hara energies. First, we slightly generalize the O'Hara energies and consider a characterization of its finiteness. The finiteness of the O'Hara energies was considered by Blatt in 2012 who used the Sobolev-Slobodeckij space, and naturally we consider a generalization of this space. Another fundamental problem is to understand the minimizers of the O'Hara energies. This problem has been addressed in several papers, some of them based on numerical computations. In this direction, we discuss a discretization of the O'Hara energies and give some examples of numerical computations. Particular one of the O'Hara energies, called the Möbius energy thanks to its Möbius invariance, was considered by Kim-Kusner in 1993, and Scholtes in 2014 established convergence properties. We apply their argument in general since the argument does not rely on Möbius invariance. [ABSTRACT FROM AUTHOR]

A remarkable theorem of Besicovitch is that an integrable function ƒ on R2 is strongly differentiable if its associated strong maximal function MS ƒ is finite a.e. We provide an analogue of Besicovitch's result in the context of ergodic theory that provides a generalization of Birkhoff's Ergodic Theorem. In particular, we show that if ƒ is a measurable function on a standard probability space and T is an invertible measure-preserving transformation on that space, then the ergodic averages of f with respect to T converge a.e. if and only if the associated ergodic maximal function T*ƒ is finite a.e. [ABSTRACT FROM AUTHOR]

In this paper, we study the action of Homeo0(M), the identity component of the group of homeomorphisms of an n‐dimensional manifold M with an Fp‐free action, on another manifold N of dimension n+k<2n. We prove that if M is not an Fp‐homology sphere, then N≅M×K for a homology manifold K such that the action of Homeo0(M) on M is natural and on K is trivial. We also prove that when M=Sn a sphere, any nontrivial action is a generalization of the 'coning‐off' construction. [ABSTRACT FROM AUTHOR]

We show that in a category with pullbacks, arbitrary sifted colimits may be constructed as filtered colimits of reflexive coequalizers. This implies that "lex sifted colimits", in the sense of Garner-Lack, decompose as Barr-exactness plus filtered colimits commuting with finite limits. We also prove generalizations of these results for k-small sifted and filtered colimits, and their interaction with k-small limits in place of finite ones, generalizing Garner's characterization of algebraic exactness in the sense of Ad'amek-Lawvere-Rosick'y. Along the way, we prove a general result on classes of colimits, showing that the k-small restriction of a saturated class of colimits is still "closed under iteration". [ABSTRACT FROM AUTHOR]

We consider the interpretation and the numerical construction of the inverse branches of n factor Blaschke-products on the disk D and show that these provide a generalization of the n-th root function. The inverse branches can be defined on pairwise disjoint regions, whose union provides the disk. An explicit formula can be given for the n factor Blaschke-products on the torus, which can be used to provide the inverse branches on T. The inverse branches can be thought of as the solutions z = zt(r) (0 ≥ r ≥ 1) to the equation B(z) = reit, where B denotes an n factor Blaschke-product. We show that starting from a known value zt(1), any zt(r) point of the solution trajectory can be reached in finite steps. The appropriate grouping of the trajectories leads to two natural interpretations of the inverse branches (see Figure 2). We introduce an algorithm which can be used to find the points of the trajectories. [ABSTRACT FROM AUTHOR]

We introduce a generalization £d(α)(X) of the finite polylogarithms £d(0)(X) = £d(X) = ∑k = 1p − 1Xk/kd, in characteristic p, which depends on a parameter α. The special case £1(α)(X) was previously investigated by the authors as the inverse, in an appropriate sense, of a parametrized generalization of the truncated exponential which is instrumental in a grading switching technique for nonassociative algebras. Here, we extend such generalization to £d(α)(X) in a natural manner and study some properties satisfied by those polynomials. In particular, we find how the polynomials £d(α)(X) are related to the powers of £1(α)(X) and derive some consequences. [ABSTRACT FROM AUTHOR]

We give a purely combinatorial proof of a special case of the Deuber-Hindman theorem which is a two-fold generalization of Schur's extension of van derWaerden's theorem and Hindman's theorem. We also give a tower bound for a finite version of it. [ABSTRACT FROM AUTHOR]

The paper uses Iwasawa theory at the prime p = 2 to prove non-vanishing theorems for the value at s = 1 of the complex L-series of certain quadratic twists of the Gross family of elliptic curves with complex multiplication by the field K = Q(v -q), where q is any prime = 7 mod 8. Our results establish some broad generalizations of the non-vanishing theorem first proven by Rohrlich using complex analytic methods. Such non-vanishing theorems are important because it is known that they imply the finiteness of the Mordell-Weil group and the Tate-Shafarevich group of the corresponding elliptic curves over the Hilbert class field of K. It is essential for the proofs to study the Iwasawa theory of the higher dimensional abelian variety with complex multiplication which is obtained by taking the restriction of scalars to K of the particular elliptic curve with complex multiplication introduced by Gross. [ABSTRACT FROM AUTHOR]

A new generalization of Lomax distribution is derived and studied. Some of its useful properties are derived. A simple clayton copula is used to generate many bivariate and multivariate type models. We performed graphical simulations to assess the finite sample behavior of the estimations. The new model is employed in modelling three real data sets. [ABSTRACT FROM AUTHOR]

Weyl's asymptotic formula states that in the semiclassical limit h ↓ 0, the sum Tr [ − h 2 Δ + V ] − of negative eigenvalues of a Schrödinger operator is given by L d cl h − d ∫ [ V ] − 1 + d / 2 and an error of order o(h−d), whenever the integral of [ V ] − 1 + d / 2 is finite. In this paper, we show that if we are given two Schrödinger operators with potentials V1 and V2, their difference Tr [ − h 2 Δ + V 1 ] − − Tr [ − h 2 Δ + V 2 ] − still follows a semiclassical asymptotic, i.e., it is, up to o(h−d), given by L d cl h − d times the integral over the difference [ V 1 ] − 1 + d / 2 − [ V 2 ] − 1 + d / 2 if certain conditions implying the finiteness of that integral are fulfilled. This holds even if V1 and V2 do not fulfill the integrability conditions of Weyl's formula, and the traces Tr [ − h 2 Δ + V 1 ] − and Tr [ − h 2 Δ + V 2 ] − are of higher order than O(h−d) each, and it is a generalization of Weyl's formula in those cases. [ABSTRACT FROM AUTHOR]

We prove a new linear relation for multiple zeta values. This is a natural generalisation of the restricted sum formula proved by Eie, Liaw and Ong. We also present an analogous result for finite multiple zeta values. [ABSTRACT FROM AUTHOR]