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\Theta is the least ordinal \alpha with the property that there is no surjection f:\mathbb {R}\rightarrow \alpha. {\mathsf {AD}}_{\mathbb {R}} is the Axiom of Determinacy for games played on the reals. It asserts that every game of length \omega of perfect information in which players take turns to play reals is determined. An ideal \mathcal {I} on \omega _1 is \omega _1-dense if the boolean algebra {\wp }(\omega _1)/ \mathcal {I} has a dense subset of size \omega _1. We consider the theories, where \mathsf {CH} stands for the Continuum Hypothesis, \begin{gather*} \mathsf {ZFC} + \mathsf {CH} + \text {"There is an \omega _1-dense ideal on \omega _1.''}\\ \mathsf {ZF}+{\mathsf {AD}}_{\mathbb {R}} + \text {"\Theta is a regular cardinal.''}\end{gather*} The main result of this paper is that the first theory given above implies the existence of a class model of the second theory given above. Woodin, in unpublished work, showed that the consistency of the second equation given above implies the consistency of the first equation given above. We will also give a proof of this result, which, together with our main theorem, establish the equiconsistency of both the equations given above. As a consequence, this resolves part of question 12 of W. Hugh Woodin [ The axiom of determinacy, forcing axioms, and the nonstationary ideal , Walter de Gruyter & Co., Berlin, 1999], in particular, it shows that the theories (b) and (c) in question 12 of W. Hugh Woodin [ The axiom of determinacy, forcing axioms, and the nonstationary ideal , Walter de Gruyter & Co., Berlin, 1999] are equiconsistent. Thus, our work completes the work that was started by Woodin and Ketchersid in [ Toward AD(\mathbb {R}) from the continuum hypothesis and an \omega _1-dense ideal , ProQuest LLC, Ann Arbor, MI, 2000] some 25 years ago. We also establish other theorems of similar nature in this paper, showing the equiconsistency of the second equation given above and the statement that the non-stationary ideal on {\wp }_{\omega _1}(\mathbb {R}) is strong and pseudo-homogeneous. The aforementioned results are the only known equiconsistency results at the level of \mathsf {AD}_{\mathbb {R}} + \text {"Θ is a regular cardinal.''} [ABSTRACT FROM AUTHOR]

In this paper, we investigate the relationships between the cardinalities of the set of injections, the set of surjections, and the set of all functions on a set which is of cardinality m$\mathfrak {m}$, denoted by I(m)$I(\mathfrak {m})$, J(m)$J(\mathfrak {m})$ and mm$\mathfrak {m}^\mathfrak {m}$, respectively. Among our results, we show that “seq1−1(m)≠I(m)≠seq(m)$\operatorname{seq}^{1-1}(\mathfrak {m})\ne I(\mathfrak {m})\ne \operatorname{seq}(\mathfrak {m})$”, “seq1−1(m)≠J(m)≠seq(m)$\operatorname{seq}^{1-1}(\mathfrak {m})\ne J(\mathfrak {m})\ne \operatorname{seq}(\mathfrak {m})$” and “seq1−1(m)

Similar to (asymptotic) average shadowing but regardless of the order of points in orbits, the notion of (asymptotic) quasi-shadowing is introduced and studied with the aid of mean orbital pseudo-metric. The asymptotic quasi-shadowing property is stronger than the quasi-shadowing property. The quasi-shadowing property with surjection implies chain transitivity. Each uniquely ergodic system has the asymptotic quasi-shadowing property. For systems with the asymptotic quasi-shadowing property, every invariant measure has generic points. Additionally, we give an equivalent characterization of the existence of generic points for every invariant measure. [ABSTRACT FROM AUTHOR]

In this paper, we study mixed Hodge structures on the cohomology of locally symmetric varieties and give an application to modular forms. After proving vanishing of some Hodge numbers, we focus on the weight filtration on the last Hodge subspace of the middle degree cohomology. We prove that the weight filtration coincides with the corank filtration on the space of modular forms of canonical weight defined by the Siegel operators, and calculate the graded quotients. As an application, we deduce surjectivity of the total Siegel operators in many cases, and identify an obstruction space in the remaining case. [ABSTRACT FROM AUTHOR]

The main goal of most static analyses is to prove the absence of bugs: if the analysis reports no alarms, then the program will not exhibit any unwanted behaviours. For this reason, they are designed to over-approximate program behaviours and, consequently, they can report some false alarms. O'Hearn's recent work on incorrectness has renewed the interest in the use of under-approximations for bug finding, because they only report true alarms. In principle, Abstract Interpretation techniques can handle under-approximations as well as over-approximations, but, in practice, few attempts were developed for the former, notwithstanding the much wider literature on the latter. In this article, we investigate the possibility of exploiting under-approximation abstract domains for bug-finding analyses. First we restrict to consider concrete powerset domains and highlight some intuitive asymmetries between over- and under-approximations. Then, we prove that the effectiveness of abstract domains defined by under-approximation Galois connection is limited because the analysis is likely to return trivial results whenever common transfer functions are encoded in the program. To this aim, we introduce the original concepts of non-emptying functions and highly surjective function family, and we prove the nonexistence of abstract domains able to under-approximate such functions in a non-trivial way. We show many examples of finite and infinite numerical domains, as well as other generic domains. In all such cases, we prove the impossibility of performing non-trivial analyses via under-approximation Galois connections. [ABSTRACT FROM AUTHOR]

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We are devoted in this work to dealing with a class of time-fractional nonstationary incompressible Navier–Stokes–Voigt equation involving the Caputo fractional derivative. By exploiting the properties of the operators in the equation, we use the Rothe method to show the existence of weak solutions to the equation by verifying all the conditions of the surjectivity theorem for nonlinear weakly continuous operators. [ABSTRACT FROM AUTHOR]

We investigate some Bernstein–Gelfand–Gelfand complexes consisting of Sobolev spaces on bounded Lipschitz domains in R n . In particular, we compute the cohomology of the conformal deformation complex and the conformal Hessian complex in the Sobolev setting. The machinery does not require algebraic injectivity/surjectivity conditions between the input spaces, and allows multiple input complexes. As applications, we establish a conformal Korn inequality in two space dimensions with the Cauchy–Riemann operator and an additional third-order operator with a background in Möbius geometry. We show that the linear Cosserat elasticity model is a Hodge–Laplacian problem of a twisted de Rham complex. From this cohomological perspective, we propose potential generalizations of continuum models with microstructures. [ABSTRACT FROM AUTHOR]

We investigate a generalized class of fractional hemivariational inequalities involving the time-fractional aspect. The existence result is established by employing the Rothe method in conjunction with the surjectivity of multivalued pseudomonotone operators and the properties of the Clarke generalized gradient. We are also exploring a numerical approach to address the problem, utilizing both spatially semi-discrete and fully discrete finite elements, along with a discrete approximation of the fractional derivative. All these results are applied to the analysis and numerical approximations of a frictional contact model that describes the quasi-static contact between a viscoelastic body and a solid foundation. The constitutive relation is modeled using the fractional Kelvin-Voigt law. The contact and friction are described by the subdifferential boundary conditions. The variational formulation of this problem leads to a fractional hemivariational inequality. The error estimates for this problem are derived. Finally, here's a second concrete example to illustrate the application. We propose a frictional contact model that incorporates normal compliance and Coulomb friction to describe the quasi-static contact between a viscoelastic body and a solid foundation. [ABSTRACT FROM AUTHOR]

We show that each cluster seed in the augmentation variety contains an embedded exact Lagrangian filling. This resolves the matter of surjectivity of the map from Lagrangian fillings to cluster seeds. The main new technique to produce these Lagrangian fillings is the construction and study of a quiver with potential associated to curve configurations. We prove that its deformation space is trivial and show how to use it to manipulate Lagrangian fillings with L -compressing systems via Lagrangian disk surgeries. [ABSTRACT FROM AUTHOR]

We establish a general theory for projective dimensions of the logarithmic derivation modules of hyperplane arrangements. This includes an addition-deletion and a restriction theorem, a Yoshinaga type result, and a division theorem for projective dimensions of hyperplane arrangements. These new theorems are all generalizations of classical results for free arrangements, which is the special case of projective dimension zero. To prove these results, we introduce several new methods to determine the surjectivity of the Euler and the Ziegler restriction maps, which is combinatorially determined when the projective dimension is not maximal for all localizations. Also, we introduce a new class of arrangements in which the projective dimension is combinatorially determined. [ABSTRACT FROM AUTHOR]

Let K be an algebraically closed field of characteristic p ≥ 0. Assume F , F (1) , F (2) , and (F (1)) p are the free group on n > 1 generators, the first and second derived subgroups of F , and the subgroup of F (1) generated by all p -powers, respectively. In this paper, among other results, we show that for any word w ∈ F (1) ∖ F (2) (F (1)) p , the corresponding word map w : ∏ n PSL 2 (K) → PSL 2 (K) is surjective. We show that the class of such words w contains, for instance, all (weakly) Engel words. [ABSTRACT FROM AUTHOR]

Let $ \mathcal {M}_{n} $ M n be the set of $ n\times n $ n × n complex matrices, and for $ \varepsilon \gt 0 $ ε > 0 and $ A\in \mathcal {M}_{n} $ A ∈ M n , let $ \sigma _{\varepsilon }(A) $ σ ε (A) denote the $ \varepsilon - $ ε − pseudo spectrum of A. Maps Φ on $ \mathcal {M}_{n} $ M n which preserve the skew Lie product of matrices in a sense that \[ \sigma_{\varepsilon}(\Phi(A)\Phi(B) - \Phi(B)\Phi(A)^{*})=\sigma_{\varepsilon}(AB - BA^{*})\quad (A, B\in\mathcal{M}_{n}) \] σ ε (Φ (A) Φ (B) − Φ (B) Φ (A) ∗) = σ ε (AB − B A ∗) (A , B ∈ M n) are characterized, with no surjectivity assumption on them. Analogous description for the skew product on matrices is also noted. [ABSTRACT FROM AUTHOR]

The article discusses the comparative size of sets A and B, focusing on three main questions regarding their relative sizes based on injections and surjections. Topics include the injective account versus the surjective account of set size, the implications of the axiom of choice on these accounts, and the challenges to Cantor's definitions of cardinality.

Let X be a uniformly smooth Banach space and let T, A be hemicontinuous operators defined on X with values in X. Suppose, in addition, that T is strongly pseudo-contractive (with constant k > 0) while cI+A is accretive for 0 < c < 1-k. Then the operator T-A has a unique fixed point, which represents a significant extension of the main theorem in [12]. Some surjectivity results are also discussed, which are related to the main result. In particular, we begin with a surjectivity result for monotone operators defined on reflexive Banach spaces. [ABSTRACT FROM AUTHOR]

Over the past two decades, significant advancements have been made in understanding the stability according to Hyers–Ulam involving different functional equations (FEs). This study investigates the generalized stability of norm-based (norm-additive) FEs within the framework of arbitrary (noncommutative) groups and p-uniformly convex spaces. Specifically, we analyze two key functional equations, ∥ η (g h) ∥ = ∥ η (g) + η (h) ∥ and ∥ η (g h − 1) ∥ = ∥ η (g) − η (h) ∥ for every g , h ∈ G , where (G , ·) denotes an arbitrary group and B is considered to be a p-uniformly convex space. The surjectivity of the function η : G → B is a critical assumption in our analysis. Drawing upon the foundational works of L. Cheng and M. Sarfraz, this paper applies the large perturbation method tailored for p-uniformly convex spaces, where p ≥ 1 . This study extends previous research by offering a deeper exploration of the conditions under which these functional equations demonstrate Hyers–Ulam stability. In this study, the additive functional equation demonstrates a fundamental form of symmetry, where the order of operands does not affect the results. This symmetry under permutation of arguments is crucial for the analysis of stability. In the context of norm-additive FEs, this stability criterion investigates how small changes in the inputs of a functional equation affect the outputs, especially when the function is expected to follow an additive form. [ABSTRACT FROM AUTHOR]

If X is a smooth projective variety over ₹, the Hodge D-conjecture of Beilinson asserts the surjectivity of the regulator map to Deligne cohomology with real coefficients. It is known to be false in general, but is true in some special cases like Abelian surfaces and K3-surfaces -- and still expected to be true when the variety is defined over a number field. We prove an analogue of this for Abelian surfaces at a non-Archimedean place where the surface has bad reduction. Here, the Deligne cohomology is replaced by a certain Chow group of the special fibre. The case of good reduction is harder and was first studied by Spiess (1999) in the case of products of elliptic curves and by the author in general (Sreekantan, 2014). The case of bad reduction was also studied by the author in Sreekantan (2008). [ABSTRACT FROM AUTHOR]

The main goal of this research article is to investigate the stability of generalized norm-additive functional equations. This study demonstrates that these equations are Hyers-Ulam stable for surjective functions from an arbitrary group G to a real Banach space B using the large perturbation method. Furthermore, hyperstability results are investigated for a generalized Cauchy equation. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a class of second-order evolutionary history-dependent variational–hemivariational inequalities with constraint. The unique solvability of the considered second-order evolutionary inequality problem is established via a surjectivity result combined with a fixed point theorem. Moreover, we construct a regularized problem for such second-order evolutionary history-dependent variational–hemivariational inequality and show the convergence of the regularized solutions toward the solution of the original problem under some mild assumptions. [ABSTRACT FROM AUTHOR]

Let (R,\mathfrak {m}_R,\mathbb {k}) be a one-dimensional complete local reduced \mathbb {k}-algebra over a field of characteristic zero. The ring R is said to be quasihomogeneous if there exists a surjection \Omega _R\twoheadrightarrow \mathfrak {m} where \Omega _R denotes the module of differentials. We present two characterizations of quasihomogeniety of R in the case when R is a domain. The first one on the valuation semigroup of R and the other on the trace ideal of the module \Omega _R. [ABSTRACT FROM AUTHOR]

Guzide Senel first time introduced the concept of soft distance functions between two soft points in soft metric spaces. Motivated by the study of Senel on soft metric spaces, we have define the new definition of soft isometries with soft points and to investigate some important prepositions on soft isometries. Moreover, we also introduce the examples depend on soft isometries. We hope that this result will provide a good and fruitful results for beginners and also help for some new results for researcher in the field of soft isometric spaces. [ABSTRACT FROM AUTHOR]

We define an E ∞ -coalgebra structure on the chains of multisimplicial sets. Our primary focus is on the surjection chain complexes of McClure-Smith, for which we construct a zig-zag of complexity preserving quasi-isomorphisms of E ∞ -coalgebras relating them to both the singular chains on configuration spaces and the Barratt–Eccles chain complexes. [ABSTRACT FROM AUTHOR]

We give sufficient conditions for the surjectivity of higher Gaussian maps on a polarized K3 surface. As an application, we show that the |$k$| -th Gaussian map for a general curve of genus |$g$| (that depends quadratically with |$k$|⁠) is surjective. Along the proof, we also exhibit an ampleness criterion for divisors in the Hilbert scheme of two points of a K3 surface. [ABSTRACT FROM AUTHOR]

Let A be a regular ring of dimension d essentially of finite type over an infinite field k of characteristic ≠2. Let P be a projective A -module of rank n with 2 n ≥ d + 3. Let I be an ideal of A [ T ] of height n and ϕ : P [ T ] ↠ I / I 2 be a surjection. If ϕ ⊗ A (T) has a surjective lift θ : P [ T ] ⊗ A (T) ↠ I A (T) , then ϕ has a surjective lift Φ : P [ T ] ↠ I. The case P = A n is due to Das-Tikader-Zinna [7]. [ABSTRACT FROM AUTHOR]

In the paper we provide systematic approaches to study existence and feedback control for a new evolutionary equation involving pseudomonotone operators. We first establish several existence results for the evolutionary equation by exploiting the Rothe method and using a surjectivity result for multivalued pseudomonotone operators. Then we show the existence of feasible pairs for the feedback control problem by assuming some sufficient conditions. Moreover, the existence of solutions to an evolutionary hemivariational inequality is presented. [ABSTRACT FROM AUTHOR]

The loop group |$G((z^{-1}))$| of a simple complex Lie group |$G$| has a natural Poisson structure. We introduce a natural family of Poisson commutative subalgebras |$\overline{{\textbf{B}}}(C) \subset{{\mathcal{O}}}(G((z^{-1}))$| depending on the parameter |$C\in G$| called classical universal Bethe subalgebras. To every antidominant cocharacter |$\mu $| of the maximal torus |$T \subset G$|⁠ , one can associate the closed Poisson subspace |${{\mathcal{W}}}_{\mu }$| of |$G((z^{-1}))$| (the Poisson algebra |${{\mathcal{O}}}({{\mathcal{W}}}_{\mu })$| is the classical limit of so-called shifted Yangian |$Y_{\mu }(\mathfrak{g})$| defined in [ 1 , Appendix B]). We consider the images of |$\overline{{\textbf{B}}}(C)$| in |${{\mathcal{O}}}({{\mathcal{W}}}_{\mu })$|⁠ , denoted by |$\overline{B}_{\mu }(C)$|⁠ , that should be considered as classical versions of (not yet defined in general) Bethe subalgebras in shifted Yangians. For regular |$C$| centralizing |$\mu $|⁠ , we compute the Poincaré series of these subalgebras. For |$\mathfrak{g}=\mathfrak{g}\mathfrak{l}_{n}$|⁠ , we define the natural quantization |${\textbf{Y}}^{\textrm{rtt}}(\mathfrak{g}\mathfrak{l}_{n})$| of |${{\mathcal{O}}}(\operatorname{Mat}_{n}((z^{-1})))$| and universal Bethe subalgebras |${\textbf{B}}(C) \subset{\textbf{Y}}^{\textrm{rtt}}(\mathfrak{g}\mathfrak{l}_{n})$|⁠. Using the RTT realization of |$Y_{\mu }(\mathfrak{g}\mathfrak{l}_{n})$| (invented by Frassek, Pestun, and Tsymbaliuk), we obtain the natural surjections |${\textbf{Y}}^{\textrm{rtt}}(\mathfrak{g}\mathfrak{l}_{n}) \twoheadrightarrow Y_{\mu }(\mathfrak{g}\mathfrak{l}_{n})$|⁠ , which quantize the embedding |${{\mathcal{W}}}_{\mu } \subset \operatorname{Mat}_{n}((z^{-1}))$|⁠. Taking the images of |${\textbf{B}}(C)$| in |$Y_{\mu }(\mathfrak{g}\mathfrak{l}_{n})$|⁠ , we recover Bethe subalgebras |$B_{\mu }(C) \subset Y_{\mu }(\mathfrak{g}\mathfrak{l}_{n})$| proposed by Frassek, Pestun, and Tsymbaliuk. [ABSTRACT FROM AUTHOR]

For linear non-uniform cellular automata (NUCA) which are global perturbations of CA over an arbitrary universe, we introduce and investigate their dual linear NUCA, which are also endomorphisms over a generally infinite dimensional vector space. Generalizing results for linear CA, we show that dynamical properties namely pre-injectivity, resp. injectivity, resp. stably injectivity, resp. invertibility of a linear NUCA is equivalent to surjectivity, resp. post-surjectivity, resp. stably post-surjectivity, resp. invertibility of the dual linear NUCA. However, while bijectivity is a dual property for linear CA, it is no longer the case for linear NUCA. We prove that for linear NUCA, stable injectivity and stable post-surjectivity are precisely characterized respectively by left invertibility and right invertibility and that a linear NUCA is invertible if and only if it is pre-injective and stably post-surjective. Surprisingly, we show that linear NUCA with finite memory satisfy the shadowing property also known as the pseudo-orbit tracing property. Thus, linear NUCA can be useful for fault-tolerant computation. Applications on the dual surjunctivity are also obtained. [ABSTRACT FROM AUTHOR]

In symmetric cryptography, block ciphers, stream ciphers and permutations often make use of a round function and many round functions consist of a linear and a non-linear layer. One that is often used is based on the cellular automaton that is denoted by χ as a Boolean map on bi-infinite sequences, F 2 Z . It is defined by σ ↦ ν where each ν i = σ i + (σ i + 1 + 1) σ i + 2 . A map χ n is a map that operates on n-bit arrays with periodic boundary conditions. This corresponds with χ restricted to periodic infinite sequences with period that divides n. This map χ n is used in various permutations, e.g., Keccak-f (the permutation in SHA-3), ASCON (the NIST standard for lightweight cryptography), Xoodoo, Rasta and Subterranean (2.0). In this paper, we characterize the graph of χ on periodic sequences. It turns out that χ is surjective on the set of all periodic sequences. We will show what sequences will give collisions after one application of χ . We prove that, for odd n, the order of χ n (in the group of bijective maps on F 2 n ) is 2 ⌈ lg (n + 1 2) ⌉ . A given periodic sequence lies on a cycle in the graph of χ , or it can be represented as a polynomial. By regarding the divisors of such a polynomial one can see whether it lies in a cycle, or after how many iterations of χ it will. Furthermore, we can see, for a given σ , the length of the cycle in its component in the state diagram. Finally, we extend the surjectivity of χ to F 2 Z , thus to include non-periodic sequences. [ABSTRACT FROM AUTHOR]

We prove the surjectivity part of Goncharov's depth conjecture over a quadratically closed field. We also show that the depth conjecture implies that multiple polylogarithms of depth d and weight n can be expressed via a single function Li n - d + 1 , 1 , ⋯ , 1 (a 1 , a 2 , ⋯ , a d) , and we prove this latter statement for d = 2 . [ABSTRACT FROM AUTHOR]

Let K be a field of characteristic 0, let S be a complete local ring with coefficient field K , let K [ [ x 1 , ... , x n ] ] be the ring of formal power series in variables x 1 , ... , x n with coefficients from K , let K [ [ x 1 , ... , x n ] ] → S be a K -algebra surjection and let E • • , • be the associated Hodge-de Rham spectral sequence for the computation of the de Rham homology of S. Nicholas Switala [12] proved that this spectral sequence is independent of the surjection beginning with the E 2 page, and the groups E 2 p , q are all finite-dimensional over K. In this paper we extend this result to affine varieties. Namely, let Y be an affine variety over K , let X be a non-singular affine variety over K , let Y ⊂ X be an embedding over K and let E • • , • be the associated Hodge-de Rham spectral sequence for the computation of the de Rham homology of Y. Then this spectral sequence is independent of the embedding beginning with the E 2 page, and the groups E 2 p , q are all finite-dimensional over K. [ABSTRACT FROM AUTHOR]

The aim of the paper is to study a coupled system which consists of a fractional differential hemivariational inequality (FDHVI, for short) combined with a fractional hemivariational inequality (FHVI, for short). By utilizing Rothe method and surjectivity result, the existence of coupled system is established. In addition, we apply the results to a new quasistatic contact problem, in which the constitutive equations are described by the fractional Kelvin-Voigt laws. [ABSTRACT FROM AUTHOR]

The aim of the paper is to study a new class of coupled variational–hemivariational inequalities with unilateral constraints and history‐dependent operators. First, by employing a fixed‐point theorem for history‐dependent operators combined with surjectivity theorem, we establish the existence and uniqueness of solution for coupled system. Second, we obtain a convergence result, namely, related penalized problems of solutions converge to the solution to the original system. Finally, we conclude with a new contact problem of the body pressure of two elastic materials. [ABSTRACT FROM AUTHOR]

We study minimisers of the p-conformal energy functionals, E p (f) : = ∫ D K p (z , f) d z , f | S = f 0 | S , defined for self mappings f : D → D with finite distortion and prescribed boundary values f 0 . Here K (z , f) = ‖ D f (z) ‖ 2 J (z , f) = 1 + | μ f (z) | 2 1 - | μ f (z) | 2 is the pointwise distortion functional and μ f (z) is the Beltrami coefficient of f. We show that for quasisymmetric boundary data the limiting regimes p → ∞ recover the classical Teichmüller theory of extremal quasiconformal mappings (in part a result of Ahlfors), and for p → 1 recovers the harmonic mapping theory. Critical points of E p always satisfy the inner-variational distributional equation 2 p ∫ D K p μ f ¯ 1 + | μ f | 2 φ z ¯ d z = ∫ D K p φ z d z , ∀ φ ∈ C 0 ∞ (D). We establish the existence of minimisers in the a priori regularity class W 1 , 2 p p + 1 (D) and show these minimisers have a pseudo-inverse - a continuous W 1 , 2 (D) surjection of D with (h ∘ f) (z) = z almost everywhere. We then give a sufficient condition to ensure C ∞ (D) smoothness of solutions to the distributional equation. For instance K (z , f) ∈ L loc p + 1 (D) is enough to imply the solutions to the distributional equation are local diffeomorphisms. Further K (w , h) ∈ L 1 (D) will imply h is a homeomorphism, and together these results yield a diffeomorphic minimiser. We show such higher regularity assumptions to be necessary for critical points of the inner variational equation. [ABSTRACT FROM AUTHOR]

The concepts of soft faint continuity as a weaker form of soft weak continuity and soft faint θ ω -continuity as a weaker form of soft weak θ ω -continuity are introduced. Numerous characterizations of them are given. We further demonstrate that, under soft restrictions, they are retained. Moreover, we show that a soft function is soft faintly continuous (respectively, soft faintly θ ω -continuous) if its soft graph function is soft faintly continuous (respectively, soft faintly θ ω -continuous). In addition, we show that a soft function with a soft almost regular (respectively, soft extremally disconnected) co-domain is soft faintly continuous iff it is soft almost continuous (respectively, soft δ -continuous). Furthermore, we show that soft faintly continuous surjective functions are soft set-connected functions, and as a corollary, we demonstrate how soft faintly continuous functions sustain soft connectivity. Finally, we studied the symmetry between our new notions and their topological counterparts. [ABSTRACT FROM AUTHOR]

A classification is a surjective mapping from a set of objects to a set of categories. A classification aggregation function aggregates every vector of classifications into a single one. We show that every citizen sovereign and independent classification aggregation function is essentially a dictatorship. This impossibility implies an earlier result of Maniquet and Mongin (2016), who show that every unanimous and independent classification aggregation function is a dictatorship. The relationship between the two impossibilities is reminiscent to the relationship between Wilson's (1972) and Arrow's (1951) impossibilities in preference aggregation. Moreover, while the Maniquet-Mongin impossibility rests on the existence of at least three categories, we propose an alternative proof technique that covers the case of two categories, except when the number of objects is also two. We also identify all independent and unanimous classification aggregation functions for the case of two categories and two objects. • Classification Aggregation has a strong relation with preference aggregation. • We prove an equivalent of Wilson's impossibility theorem. • Surjectivity and Independence both play an important role for the impossibility. [ABSTRACT FROM AUTHOR]

We consider weighted composition operators, that is operators of the type g ↦ w · g ∘ f , acting on spaces of Lipschitz functions. Bounded weighted composition operators, as well as some compact weighted composition operators, have been characterized quite recently. In this paper, we provide a different approach involving their pre-adjoint operators, namely the weighted Lipschitz operators acting on Lipschitz free spaces. This angle allows us to retrieve and sometimes improve some results from the literature. Notably, we obtain a distinct characterization of boundedness with a precise estimate of the norm. We also characterise injectivity, surjectivity, compactness and weak compactness in full generality. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of surjective radical parametrization and we prove sufficient conditions for a radical curve parametrization to be surjective. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the discussion of a new dynamical system involving a history-dependent variational-hemivariational inequality coupled with a non-linear evolution equation. The existence and uniqueness of the solution to this problem are established using the Rothe method and a surjectivity result for a pseudo-monotone perturbation of a maximal operator. Additionally, we derive the regularity solution for such a history-dependent variational-hemivariational inequality. Furthermore, the main results obtained in this study are applied to investigate the unique solvability of a dynamical viscoelastic frictional contact problem with long memory and wear. [ABSTRACT FROM AUTHOR]

We prove that the $p^\infty$ -torsion of the transcendental Brauer group of an abelian variety over a finitely generated field of characteristic $p>0$ is bounded. This answers a (variant of a) question asked by Skorobogatov and Zarhin for abelian varieties. To do this, we prove a 'flat Tate conjecture' for divisors. We also study other geometric Galois-invariant $p^\infty$ -torsion classes of the Brauer group which are not in the transcendental Brauer group. These classes, in contrast with our main theorem, can be infinitely $p$ -divisible. We explain how the existence of these $p$ -divisible towers is naturally related to the failure of surjectivity of specialisation morphisms of Néron–Severi groups in characteristic $p$. [ABSTRACT FROM AUTHOR]

It was proved by S. Mazur and S. Ulam in 1932 that every isometric surjection between normed real vector spaces is affine. We generalize the Mazur–Ulam theorem and find necessary and sufficient conditions under which distance-preserving mappings between seminormed real vector spaces are linear. [ABSTRACT FROM AUTHOR]

We study the Fano variety of k-planes Ω X (k) of a complete intersection X and show the surjectivity of the cylinder homomorphism in this setting, proving along the way the (classical) Hodge conjecture in cases where a numerical condition is satisfied. In particular, a new case is discovered in dimension 6. This work is a generalization of the second author's paper Motives of some Fano varieties. [ABSTRACT FROM AUTHOR]

On a locally $\lambda$ -presentable symmetric monoidal closed category $\mathcal {V}$ , $\lambda$ -ary enriched equational theories correspond to enriched monads preserving $\lambda$ -filtered colimits. We introduce discrete $\lambda$ -ary enriched equational theories where operations are induced by those having discrete arities (equations are not required to have discrete arities) and show that they correspond to enriched monads preserving preserving $\lambda$ -filtered colimits and surjections. Using it, we prove enriched Birkhof-type theorems for categories of algebras of discrete theories. This extends known results from metric spaces and posets to general symmetric monoidal closed categories. [ABSTRACT FROM AUTHOR]

Extending a result of Schröer on a Grothendieck question in the context of complex analytic spaces, we prove that the surjectivity of the Brauer map δ:Br(X)→Hét2(X,Gm,X)tors$\delta : \operatorname{Br}(X) \rightarrow H_{{\text{\rm \'{e}t}}}^2(X, \mathbb {G}_{m, X})_{\rm tors}$ for schemes depends on their étale homotopy type. We use properties of algebraic K(π,1)$K(\pi , 1)$ spaces to apply this to some classes of proper and smooth algebraic schemes. In particular, we recover a result of Hoobler and Berkovich for abelian varieties. [ABSTRACT FROM AUTHOR]

In this paper, we prove a local surjection theorem with continuous right-inverse for maps between Banach spaces, and we apply it to a class of inversion problems with loss of derivatives. [ABSTRACT FROM AUTHOR]

A necessary and sufficient condition is established for the closedness of the range or surjectivity of a differential operator acting on smooth sections of vector bundles. For connected noncompact manifolds it is shown that these conditions are derived from the regularity conditions and the unique continuation property of solutions. An application of these results to elliptic operators (more precisely, to operators with a surjective principal symbol) with analytic coefficients, to second-order elliptic operators on line bundles with a real leading part, and to the Hodge–Laplace–de Rham operator is given. It is shown that the top de Rham (respectively, Dolbeault) cohomology group on a connected noncompact smooth (respectively, complex-analytic) manifold vanishes. For elliptic operators, we prove that solvability in smooth sections implies solvability in generalized sections. [ABSTRACT FROM AUTHOR]

This paper is a systematic approach to the construction of coronas (i.e. Higson dominated boundaries at infinity) of combable spaces. We introduce three additional properties for combings: properness, coherence and expandingness. Properness is the condition under which our construction of the corona works. Under the assumption of coherence and expandingness, attaching our corona to a Rips complex construction yields a contractible σ -compact space in which the corona sits as a Z -set. This results in bijectivity of transgression maps, injectivity of the coarse assembly map and surjectivity of the coarse co-assembly map. For groups we get an estimate on the cohomological dimension of the corona in terms of the asymptotic dimension. Furthermore, if the group admits a finite model for its classifying space B G , then our constructions yield a Z -structure for the group. [ABSTRACT FROM AUTHOR]

In this paper, we study a mathematical model that describes the dynamic frictional contact between the thermoviscoelastic body and the foundation. The contact condition is modeled by the so-called nonsmooth interface law involving unilateral constraints and subdifferential inclusions. The weak formulation of our mathematical model is a coupled system containing both parabolic and hyperbolic variational-hemivariational inequalities. As a result, we deliver its unique solvability by employing a surjectivity theorem for pseudomonotone operators, a fixed point argument for history-dependent operators and a mixed equilibrium formulation with suitably selected functions. [ABSTRACT FROM AUTHOR]

This paper is concerned with the study of a parametric anisotropic double phase free boundary problem (DPFBP, for short) involving $ (p(\cdot),q(\cdot)) $-Laplacian, convection term (a reaction term depending on the gradient), and two parameters $ (\theta,\lambda) $ appearing in $ q(\cdot) $-Laplacian and convection term, respectively. The $ (p(\cdot),q(\cdot)) $-Laplace operator in (DPFBP) is considered to be controlled by two highly nonlinear and nonlocal functions. First, we apply a surjectivity theorem for pseudomonotone operators with a maximal monotone perturbation and the theory of nonsmooth analysis to examine the nonemptiness and compactness of weak solution set to (DPFBP). Then, we explore the asymptotic behavior of solution set to (DPFBP), as the parameters $ \theta $ and $ \lambda $ vary in appropriate ranges. Finally, a stability result to (DPFBP) is provided, when the obstacle function is approximated by a convergent sequence. [ABSTRACT FROM AUTHOR]