Search

In this paper, we first obtain a refined version of the Bohr inequality of norm-type for holomorphic mappings with lacunary series on the polydisk in $ \mathbb {C}^n $ C n under some restricted conditions. Next, we determine the refined version of the Bohr inequality for holomorphic functions defined on a balanced domain G of a complex Banach space X and take values in the unit disk $ \mathbb {D} $ D . Furthermore, as a consequence of one of these results, we obtain a refined version of the Bohr-type inequality for harmonic functions $ f=h+\bar {g} $ f = h + g ¯ defined on a balanced domain $ G\subset X $ G ⊂ X. All the results are proved to be sharp. [ABSTRACT FROM AUTHOR]

In this paper, we propose numerical methods for the Riesz space distributed-order advection–diffusion equation with delay in 2D. We utilize the fractional backward differential formula method of second order (FBDF2), and weighted and shifted Grünwald difference (WSGD) operators to approximate the Riesz fractional derivative and develop the finite difference method for the RFADED. It has been shown that the obtained schemes are unconditionally stable and convergent with the accuracy of O (h 2 + k 2 + κ 2 + σ 2 + ρ 2) , where h, k and κ are space step for x, y and time step, respectively. Also, numerical examples are constructed to demonstrate the effectiveness of the numerical methods, and the results are found to be in excellent agreement with analytic exact solution. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of finding the order 0<α<1$$ 0<\alpha <1 $$ in the fractional discrete system: C∇αun=Aun,n≥1,u0=x0,$$ \left\{\begin{array}{cll}{\kern0.1em }_C{\nabla}^{\alpha }{u}^n& =& A{u}^n,\kern0.30em n\ge 1,\\ {}{u}^0& =& {x}_0,\end{array}\right. $$where A$$ A $$ is a closed linear operator defined in a Banach space X,x0∈X$$ X,{x}_0\in X $$, and C∇αun$$ {\kern0.1em }_C{\nabla}^{\alpha }{u}^n $$ is the discrete Caputo fractional derivative of a given vector‐valued sequence (un)n∈ℕ0$$ {\left({u}^n\right)}_{n\in {\mathrm{\mathbb{N}}}_0} $$. [ABSTRACT FROM AUTHOR]

The symbol TD(X) denotes the hyperspace of all nonempty totally disconnected compact subsets of a Hausdorff space X. This hyperspace is endowed with the Vietoris topology. For a mapping between Hausdorff spaces f : X → Y, define the induced mapping TD(f) : TD(X) → TD(Y) by TD(f)(A) = f(A) (the image of A under f). In the current paper, we study the relationships between the condition f belongs to a class of mappings between Hausdorff spaces 필 and the condition TD(f) belongs to 필. [ABSTRACT FROM AUTHOR]

The famous Ascoli-Arzelà theorem served as a springboard for research into compactness in function spaces, particularly spaces of continuous functions. This paper investigates compact subsets of spaces of continuous functions endowed with topologies between the topology of pointwise convergence and the topology of uniform convergence. More precisely, this paper studies necessary and sufficient conditions for a subset to be compact in Cλ,u(X) for a locally-λ space X when λ ⊇ 퓕(X), for a hemi- λ λf-space X when λ ⊆ 퓟 퓢(X), and for a k-space X when λ ⊇ 퓚(X). This paper also studies that every bounded subset of Cλ,u(X) has compact closure for some classes of topological spaces X. [ABSTRACT FROM AUTHOR]

Let G = 핊d, d = 0, 1 or 3, act freely on a finitistic connected space X. This paper gives the cohomology classification of X if the mod 2 or rational cohomology of the orbit space X/G is isomorphic to the product of a projective space and sphere 픽ℙn קm, where 픽 = ℝ, ℂ or ℍ, respectively. For a free involution on X, a lower bound of covering dimension of the coincidence set of a continuous map f : X → ℝk is also determined. [ABSTRACT FROM AUTHOR]

If f is a continuous selection for the Vietoris hyperspace F (X) of the nonempty closed subsets of a space X, then the point f (X) ∈ X is not as arbitrary as it might seem at first glance. In this paper, we will characterise these points by local properties at them. Briefly, we will show that p = f (X) is a strong butterfly point precisely when it has a countable clopen base in ⊂ for some open set U ⊂ X \ {p} with ⊂ = U ⊂ {p}. Moreover, the same is valid when X is totally disconnected at p = f (X) and p is only assumed to be a butterfly point. This gives the complete affirmative solution to a question raised previously by the author. Finally, when p = f (X) lacks the above local base-like property, we will show that F(X) has a continuous selection h with the stronger property that h(S) = p for every closed S ⊂ X with p ∈ S. [ABSTRACT FROM AUTHOR]

We study the focusing mass-subcritical biharmonic nonlinear Schrödinger equation (BNLS) on the product space Rxd X Tyn. Following the crucial scaling arguments introduced in [Terracini, Tzvetkov, and Visciglia, Anal. PDE, 7 (2014), pp. 73--96] we establish existence and stability results for the normalized ground states of BNLS. Moreover, in the case where lower order dispersion is absent, we prove the existence of a critical mass number c0 ∈(0,∞) that sharply determines the y-dependence of the deduced ground states. In the mixed dispersion case, we encounter a major challenge as the BNLS is no longer scale-invariant and the arguments from [Terracini, Tzvetkov, and Visciglia, Anal. PDE, 7 (2014), pp. 73--96] for determining the sharp y-dependence of the ground states fail. The main novelty of the present paper is to address this difficult and interesting issue: Using a different scaling argument, we show that y-independence of ground states with small mass still holds in the case β > 0 and α ∈ (0, 4/(d + n)). Additionally, we also prove that ground states with sufficiently large mass must possess nontrivial y-dependence by appealing to some novel construction of test functions. The latter particularly holds for all parameters lying in the full mass-subcritical regime. [ABSTRACT FROM AUTHOR]

Let $ (X, T) $ (X , T) be a linear dynamical system defined on a Banach space X and $ {L_T}:{K_{{X^ * }}} \to {K_{{X^ * }}} $ L T : K X ∗ → K X ∗ be defined by $ {L_T}S = TS $ L T S = TS , where $ {K_{{X^ * }}} = \overline {span\{ \langle \cdot,{y^ * } \rangle x:{y^ * } \in {X^ * },x \in X\} } $ K X ∗ = span { 〈 ⋅ , y ∗ 〉 x : y ∗ ∈ X ∗ , x ∈ X } ¯ . This paper first obtains the equivalence of the (syndetically) weak multi-sensitive compactness between $ (X, T) $ (X , T) and $ ({K_{{X^ * }}},{L_T}) $ (K X ∗ , L T). Then, it is shown that (1) there exists a non-mean-sensitive linear dynamical system $ (X ,T) $ (X , T) satisfying that $ ({K_{{X^ * }}},{L_T}) $ (K X ∗ , L T) is mean sensitive; (2) There exists a non-topologically-transitive and weakly multi-sensitive compact system, which is not syndetically weakly multi-sensitive compact. Besides, it is proved that every weakly mixing linear dynamical system defined on a separable Banach space is weakly multi-sensitive compact. [ABSTRACT FROM AUTHOR]

Konstantin Tsiolkovsky famously stated that while the Earth serves as the birthplace of humanity, it is not a place where mankind can indefinitely remain. Perhaps during that period, the prospect of exploring the mysteries of outer space appeared to be an unattainable aspiration. However, in the present day, there are no longer any limitations, not even the sky, since human ingenuity has facilitated access to outer space for humanity. This access is not just for the purposes of research and exploration but also for economic endeavours. Until now, the commercial utilisation of outer space has advanced at a very sluggish rate. However, firms including SpaceX, Orion Span, Virgin Galactic, and Blue Origin have achieved significant advancements in the growth of the space industry. The revenue generated by various space-related endeavours has experienced a significant 73% increase over the last ten years. The global space economy, estimated to be valued at USD one trillion in the coming years, is primarily driven by commercial activities. This presents a formidable challenge to the existing national and international taxation systems. Similar to the open seas, space is also considered res communis omnium, meaning it belongs to the entire community, and presents comparable taxing challenges with potentially uncertain solutions. The three fundamental elements of every taxation regulation, such as the Organisation for Economic Co-operation and Development or the United Nations Model Double Taxation Convention, are the taxpayer's place of residence, the origin of their income, and the methods by which they generate their money. The current tax system does not have the necessary concepts and provisions to adapt to the rapid advancements in commercial space technology. This paper examines the legal issues surrounding commercial activities conducted in space, including the nature and handling of the income generated in various legal systems. It also addresses concerns such as tax avoidance and excessive taxation, emphasising the necessity for a globally coordinated approach to effectively tax commercial activities in space. • Human ingenuity has facilitated access to outer space for humanity, for the purposes of research and exploration and also for economic endeavours. • Space-related endeavours has experienced a significant 73% increase over the last ten years. • Commercial activities conducted in space require concerted action at international level. [ABSTRACT FROM AUTHOR]

Until recently space travel was considered a privilege of governmental astronauts, with the exception perhaps of a few billionaire space tourists, who had been accommodated on the International Space Station on some rare occasions. Nonetheless, with major space pioneers announcing plans for space tourism activities and after the successful launch in orbit of space tourism vehicles from the Virgin Galactic and Blue Origin companies, academic interest about human spaceflight for purposes of leisure and recreation has ignited. Taking into account that space tourism is in fact an unregulated activity, this paper will firstly examine whether space tourism activities fall under the scope of space law or under the scope of international air law, depending on the planned trajectory of the space tourism vehicle. Furthermore, the authors will attempt to draw conclusions concerning the legal implications of space tourism activities through a comparative analysis with the 1974 Athens Convention on the Carriage of Passengers and the Carriage of their Luggage by Sea. This international convention provides a great example on the regulation of touristic ventures, as it refers to commercial touristic activities realized within a res communis omnium , i. e., the high seas, similarly with touristic activities in space. Moreover, said Convention provides for a specialized regime for touristic activities and is of particular interest, since it has achieved stability and a desirable balance of interests between private tourism operators and passengers. In this connection, the authors will evaluate the provisions of the 1974 Athens Convention in comparison with the space treaties applicable to space tourism activities. Furthermore, suggestions will be made as to whether it would be appropriate and feasible to introduce in the space law realm certain rules of law similar to those of the 1974 Athens Convention, in order to facilitate growth in the space tourism sector, without compromising the safety of human spaceflight for space passengers. • The 1974 Athens Convention in comparison with the space treaties applicable to space tourism activities. • Legal analogy between space law and maritime law. • Legal regime governing space tourism activities. [ABSTRACT FROM AUTHOR]

Gálvez-Carrillo et al. [Decomposition spaces, incidence algebras and Möbius inversion III: The decomposition space of Möbius intervals, Adv. Math. 334 (2018) 544–584] constructed a decomposition space U of all Möbius intervals, as a recipient of Lawvere's interval construction for Möbius categories, and conjectured that U enjoys a certain universal property: for every Möbius decomposition space X , the space of culf functors from X to U is contractible. In this paper, we work at the level of homotopy 1-types to prove the first case of the conjecture, namely for locally discrete decomposition spaces. This provides also the first substantial evidence for the general conjecture. This case is general enough to cover all locally finite posets, Cartier–Foata monoids, Möbius categories and strict (directed) restriction species. The proof is 2-categorical. First, we construct a local strict model of U , which is then used to show by hand that the Lawvere interval construction, considered as a natural transformation, does not admit other self-modifications than the identity. [ABSTRACT FROM AUTHOR]

Inspired by locale theory, pointfree convex geometry was first proposed and studied by Yoshihiro Maruyama. In this paper, we shall continue to his work and investigate the related topics on pointfree convex spaces. Concretely, the following results are obtained: (1) A Hofmann–Lawson-like duality for pointfree convex spaces is established. (2) The M -injective objects in the category of S 0 -convex spaces are proved precisely to be sober convex spaces, where M is the class of strict maps of convex spaces; (3) A convex space X is sober iff there never exists a nontrivial identical embedding i : X ↪ Y such that its dualization is an isomorphism, and a convex space X is S D iff there never exists a nontrivial identical embedding k : Y ↪ X such that its dualization is an isomorphism. (4) A dual adjunction between the category CLat D of continuous lattices with continuous D-homomorphisms and the category CS D of S D -convex spaces with CP-maps is constructed, which can further induce a dual equivalence between CS D and a subcategory of CLat D ; (5) The relationship between the quotients of a continuous lattice L and the convex subspaces of cpt (L) is investigated and the collection Alg (Q (L)) of all algebraic quotients of L is proved to be an algebraic join-sub-complete lattice of Q (L) of all quotients of L, where cpt (L) denote the set of non-bottom compact elements of L. Furthermore, it is shown that Alg (Q (L)) is isomorphic to the collection Sob (P (cpt (L))) of all sober convex subspaces of cpt (L) ; (6) Several necessary and sufficient conditions for all convex subspaces of cpt (L) to be sober are presented. [ABSTRACT FROM AUTHOR]

The paper deals with minimum energy problems in the presence of external fields on a locally compact space X with respect to a function kernel κ satisfying the energy and consistency principles. For quite a general (not necessarily lower semicontinuous) external field f, we establish sufficient and/or necessary conditions for the existence of λ A , f minimizing the Gauss functional ∫ κ (x , y) d (μ ⊗ μ) (x , y) + 2 ∫ f d μ over all positive Radon measures μ with μ (X) = 1 , concentrated on quite a general (not necessarily closed or bounded) set A ⊂ X , thereby giving an answer to a question raised by M. Ohtsuka (J. Sci. Hiroshima Univ., 1961). Such results are specified for the Riesz kernels | x - y | α - n , 0 < α < n , on R n , n ⩾ 2 , and are illustrated by some examples. Furthermore, we provide various alternative characterizations of the minimizer λ A , f , and as a by-product we prove the continuity of both λ A , f and the modified Robin constant under the exhaustion of A by compact K ⊂ A . Along with the advantages of using perfect kernels, the analysis performed is substantially based on the author's recent theory of inner balayage on locally compact spaces (Potential Anal., 2022). The results obtained do hold and are new for many interesting kernels in classical and modern potential theory. [ABSTRACT FROM AUTHOR]

In this paper, we study the behavior of some classes of topological spaces under the influence of the functor of G-permutation degree 햲햯 G n . We prove: (a) if a space X is an r-space, then so is 햲햯 G n ⁡ X , (b) if X is a cosmic space, then so is 햲햯 G n ⁡ X , (c) if a space X is a C ⁢ (κ) -cosmic, then so is 햲햯 G n ⁡ X , (d) if a space X is an α-space, then so is 햲햯 G n ⁡ X . [ABSTRACT FROM AUTHOR]

This paper is devoted to introducing and investigating the bounded variation capacity and the perimeter in the abstract Wiener space X, thereby discovering some related inequalities. Functions of bounded variation in an abstract Wiener space X have been studied by many scholars. As the continuation of this research, we define the corresponding BV capacity cap H ⁡ (⋅) (now called abstract Wiener BV capacity) and investigate its properties. We also investigate some properties of sets of finite γ-perimeter, with γ being a Gaussian measure. Subsequently, the isocapacitary inequality associated with cap H ⁡ (⋅) is presented and we are able to show that it is equivalent to the Gaussian isoperimetric inequality. Finally, we prove that every set of finite γ-perimeter in X has mean curvature in L 1 ⁢ (X , γ) . [ABSTRACT FROM AUTHOR]

For a quasinilpotent operator T on a Banach space X , Douglas and Yang defined k x = lim sup z → 0 ln ⁡ ‖ (z − T) − 1 x ‖ ln ⁡ ‖ (z − T) − 1 ‖ for each nonzero vector x ∈ X , and call Λ (T) = { k x : x ≠ 0 } the power set of T. They proved that the power set have a close link with T 's lattice of hyperinvariant subspaces. In this paper, we compute the power set of some weighted shifts on ℓ p for 1 ≤ p < ∞. The following results are obtained: (1) If T is an injective quasinilpotent forward unilateral weighted shift on ℓ p (N) , then Λ (T) = { 1 } when k e 0 = 1 , where { e n } n = 0 ∞ be the canonical basis for ℓ p (N) ; (2) There is a class of backward unilateral weighted shifts on ℓ p (N) whose power set is [ 0 , 1 ] ; (3) There exists a bilateral weighted shift on ℓ p (Z) with power set [ 1 2 , 1 ]. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the uniform exponential stability of the system dx(t)dt=Ax(t)−ρBx(t),(ρ>0),$$ \frac{dx(t)}{dt}&#x0003D; Ax(t)-\rho Bx(t),\kern3.0235pt \left(\rho >0\right), $$ where the unbounded operator A$$ A $$ is the infinitesimal generator of a linear C0−$$ {C}_0- $$semigroup of contractions S(t)$$ S(t) $$ in a Hilbert space X$$ X $$ and B$$ B $$ is a Desch–Schappacher operator. Then we give sufficient conditions for exponential stability of the above system. The obtained stability result is then applied to prove the uniform exponential stabilization of some bilinear partial differential equations. [ABSTRACT FROM AUTHOR]

Let X , Y be two Banach spaces and f : X → Y be a standard coarse isometry. In this paper, we first show a sufficient and necessary condition for the coarse left-inverse operator of general Banach spaces to admit a linearly isometric right inverse. Furthermore, by using the well-known simultaneous extension operator, we obtain an asymptotical stability result when Y is a space of continuous functions. In addition, we also prove that every coarse left-inverse operator does admit a linear isometric right inverse without other assumptions when Y is a L p (1 < p < ∞) space, or both X and Y are finite dimensional spaces of the same dimension. Making use of the results mentioned above, we generalize several results of isometric embeddings and give a stability result of coarse isometries between Banach spaces. [ABSTRACT FROM AUTHOR]

Recently, Ludewig and Thiang introduced a notion of a uniformly localized Wannier basis with localization centers in an arbitrary uniformly discrete subset D in a complete Riemannian manifold X. They show that, under certain geometric conditions on X, the class of the orthogonal projection onto the span of such a Wannier basis in the K-theory of the Roe algebra C*(X) is trivial. In this paper, we clarify the geometric conditions on X, which guarantee triviality of the K-theory class of any Wannier projection. We show that this property is equivalent to triviality of the unit of the uniform Roe algebra of D in the K-theory of its Roe algebra, and provide a geometric criterion for that. As a consequence, we prove triviality of the K-theory class of any Wannier projection on a connected proper measure space X of bounded geometry with a uniformly discrete set of localization centers. [ABSTRACT FROM AUTHOR]

A subset A of a vector space X is called \alpha-lineable whenever A contains, except for the null vector, a subspace of dimension \alpha. If X has a topology, then A is \alpha-spaceable if such subspace can be chosen to be closed. The vast existing literature on these topics has shown that positive results for lineability and spaceability are quite common. Recently, the stricter notions of (\alpha,\beta)-lineability/spaceability were introduced as an attempt to shed light on more subtle issues. In this paper, among other results, we prove some general criteria for the notion of (\alpha,\beta)-lineability/spaceability and, as applications, we extend recent results of different authors. [ABSTRACT FROM AUTHOR]

In this paper we give a quantitative analysis of an explicit iteration method due to C.E. Chidume for the approximation of a zero of an m-accretive operator A : X → 2 X in Banach spaces which does not involve the computation of the resolvent of A. [ABSTRACT FROM AUTHOR]

In this paper, we define some combinatorial principles to characterize spaces X whose hyperspace satisfies some variation of some classical star selection principle. Specifically, the variations characterized are the selective and absolute versions of the star selection principles for the Menger and Rothberger cases; also, the hyperspaces considered in these characterizations are CL(X), 핂(X), 픽(X) and ℂ핊(X) in both cases, endowed with either the Fell topology or the Vietoris topology. [ABSTRACT FROM AUTHOR]

A study of the class \Delta consisting of topological \Delta-spaces was originated by Jerzy Ka̧kol and Arkady Leiderman [Proc. Amer. Math. Soc. Ser. B 8 (2021), pp. 86–99; Proc. Amer. Math. Soc. Ser. B 8 (2021), pp. 267–280]. The main purpose of this paper is to introduce and investigate new classes \Delta _2 \subset \Delta _1 properly containing \Delta. We observe that for every first-countable X the following equivalences hold: X\in \Delta _1 iff X\in \Delta _2 iff each countable subset of X is G_{\delta }. Thus, new proposed concepts provide a natural extension of the family of all \lambda-sets beyond the separable metrizable spaces. We prove that (1) A pseudocompact space X belongs to the class \Delta _1 iff countable subsets of X are scattered. (2) Every regular scattered space belongs to the class \Delta _2. We investigate whether the classes \Delta _1 and \Delta _2 are invariant under the basic topological operations. Similarly to \Delta, both classes \Delta _1 and \Delta _2 are invariant under the operation of taking countable unions of closed subspaces. In contrast to \Delta, they are not preserved by closed continuous images. Let Y be l-dominated by X, i.e. C_p(X) admits a continuous linear map onto C_p(Y). We show that Y \in \Delta _1 whenever X \in \Delta _1. Moreover, we establish that if Y is l-dominated by a compact scattered space X, then Y is a pseudocompact space such that its Stone–Čech compactification \beta Y is scattered. [ABSTRACT FROM AUTHOR]

The object of this paper is to show that non-homotopy finite Poincaré duality spaces are plentiful. Let π be a finitely presented group. Assuming that the reduced Grothendieck group eK 0(Z[π]) has a non-trivial 2-divisible element, we construct a finitely dominated Poincaré space X with fundamental group π such that X is not homotopy finite. The dimension of X can be made arbitrarily large. Our proof relies on a result which says that every finitely dominated space possesses a stable Poincaré duality thickening. [ABSTRACT FROM AUTHOR]

Let C be a nonempty closed bounded (not necessary convex) subset of a Banach space X and let T : C → C be an (αβ)-nonexpansive mapping with α > 0, β > 0 and α + β < 1. In this paper, we show that T has a unique fixed point. Moreover, T is a Picard operator if and only if T is asymptotically regular. [ABSTRACT FROM AUTHOR]

Within the next decade it is likely that the space tourism industry will grow and the number of humans travelling into space via commercial entities such as Virgin Galactic and Blue Origin, will increase significantly. Current space tourism ventures focus on short duration sub-orbital flights and visits to Low Earth Orbit (LEO). In the next few decades, a journey into space could become as normal as a transatlantic flight. During these new commercial ventures, the effects of cosmic radiation exposure, especially during sudden changes in space weather, such as ground level enhancement (GLE) or solar particle events (SPEs), could have significant health implications for crew and passengers. Such changes in space weather could expose space tourists to radiation doses in excess of the recommended maximum 1 mSv yearly effective dose uptake for a member of the public and 20 mSv yearly effective dose limit for those working with radiation (ICRP Publication 103, 2007 [1]). Domestic legislation and regulation focussing on potential radiation exposure for space tourists is limited and largely untested; there is heavy focus on conventional risk and wider safety, with guidance stemming from regulation of commercial high-level flights, which are significantly different to space tourism enterprises. In this paper we consider the current domestic legislation and regulations adopted by the USA and the UK, as two examples of launch nations with legislation and regulation relating to space tourism activities. We acknowledge and consider feedback we have received from the UK Civil Aviation Authority (CAA) on current regulations and topics outlined in this paper. We discuss whether current legislation and regulation offers sufficient protection for space flight participants (space tourists), and whether risk is balanced appropriately between the operators who provide space tourism services and those taking part. Finally, we discuss the routes to acceptance of the radiation risks and make recommendations for legislators, regulators and operators to support them in ensuring that the risks are managed appropriately while also supporting the development of the industry. [ABSTRACT FROM AUTHOR]

In the present paper we identify those filtered probability spaces (Ω , F , (F n) , P) that determine already the martingale type of a Banach space X. We isolate intrinsic conditions on the filtration (F n) of purely atomic σ -algebras which determine that the upper ℓ p estimates ‖ f ‖ L p (Ω , X) p ⩽ C p (‖ E (f | F 0) ‖ L p (Ω , X) p + ∑ n = 1 ∞ ‖ E (f | F n) − E (f | F n − 1) ‖ L p (Ω , X) p) , f ∈ L p (Ω , X) imply that the Banach space X is of martingale type p. Our paper complements G. Pisier's investigation [12] and continues the work by S. Geiss and second named author in [3]. [ABSTRACT FROM AUTHOR]

In this work, we are concerned with the realization of spaces up to rational homotopy as classifying spaces. In this paper, we first show that a class of rank-two rational spaces cannot be realized up to rational homotopy as the classifying space of any n -connected and π -finite space for n ≥ 1. We also show that the Eilenberg-Mac Lane space K (Q r , n) (r ≥ 2 , n ≥ 2) can be realized up to rational homotopy as the classifying space of a simply connected and elliptic space X if and only if X has the rational homotopy type of ∏ r S n − 1 with n even. [ABSTRACT FROM AUTHOR]

A large hindrance to analyzing information in genetic or protein sequence data has been a lack of a mathematical framework for doing so. In this paper, we present a multinomial probability space X as a general foundation for multicategory discrete data, where categories refer to variants/alleles of biosequences. The external information that is infused in order to generate a sample of such data is quantified as a distance on X between the prior distribution of data and the empirical distribution of the sample. A number of distances on X are treated. All of them have an information theoretic interpretation, reflecting the information that the sampling mechanism provides about which variants that have a selective advantage and therefore appear more frequently compared to prior expectations. This includes distances on X based on mutual information, conditional mutual information, active information, and functional information. The functional information distance is singled out as particularly useful. It is simple and has intuitive interpretations in terms of 1) a rejection sampling mechanism, where functional entities are retained, whereas non-functional categories are censored, and 2) evolutionary waiting times. The functional information is also a quasi-metric on X , with information being measured in an asymmetric, mountainous landscape. This quasi-metric property is also retained for a robustified version of the functional information distance that allows for mutations in the sampling mechanism. The functional information quasi-metric has been applied with success on bioinformatics data sets, for proteins and sequence alignment of protein families. [ABSTRACT FROM AUTHOR]

In a recent paper, we defined generalized color orderings (GCO) and Feynman diagrams (GFD) to compute color-dressed generalized biadjoint amplitudes. In this work, we study the Cachazo-Early-Guevara-Mizera (CEGM) representation of generalized partial amplitudes and "decoupling" identities. This representation is a generalization of the Cachazo-He-Yuan (CHY) formulation as an integral over the configuration space X (k , n) of n points on CP k − 1 in generic position. Unlike the k = 2 case, Parke-Taylor-like integrands are not enough to compute all partial amplitudes for k > 2. Here we give a set of constraints that integrands associated with GCOs must satisfy and use them to construct all (3 , n < 9) integrands, all (3 , 9) integrands up to four undetermined constants, and 95% of (4 , 8) integrands up to 24 undetermined constants. k = 2 partial amplitudes are known to satisfy identities. Among them, the so-called U (1) decoupling identities are the simplest ones. These are characterized by a label i and a color ordering in X (2 , | [ n ] ∖ { i } |). Here we introduce decoupling identities for k > 2 determined combinatorially using GCOs. Moreover, we identify the natural analog of U (1) identities as those characterized by a pair of labels i ≠ j , and a pair of GCOs, one in X (k , | [ n ] ∖ { i } |) and the other in X (k − 1 , | [ n ] ∖ { j } |). We call them double extension identities. We also provide explicit connections among different ways of representing GCOs, such as configurations of lines, configurations of points, and reorientation classes of uniform oriented matroids (chirotopes). [ABSTRACT FROM AUTHOR]

A topological space X is called almost discrete, if it has precisely one nonisolated point. In this paper, we get that for a countable product X = ∏ X i of almost discrete spaces X i the space C p (X) of all continuous real-valued functions with the topology of pointwise convergence is a μ -space if, and only if, X is a weak q -space if, and only if, t (X) = ω if, and only if, X is functionally generated by the family of all its countable subspaces. This result makes it possible to solve Archangel'skii's problem on the product of Grothendieck spaces. It is proved that in the model of ZFC , obtained by adding one Cohen real, there are Grothendieck spaces X and Y such that X × Y is not weakly Grothendieck space. In (P F A) : the product of any countable family almost discrete Grothendieck spaces is a Grothendieck space. [ABSTRACT FROM AUTHOR]

We extend some of main results of Abasov et al., 2016, Fotiy et al., (2020), Mykhaylyuk et al., (2015), Pliev and Fang, (2017), Pliev and Popov, (2014) to the setting of orthogonally additive operators on lattice-normed spaces. We introduce a new class of C -complete lattice-normed spaces which strictly includes a class of Banach–Kantorovich spaces. The first main result of the paper asserts that every laterally-to-norm continuous C -compact orthogonally additive operator T : X → Y from an atomless C -complete lattice-normed space X to a Banach space Y is narrow. As a non expecting consequence of the first main result we obtain necessary and sufficient conditions for a nonlinear superposition operator T N : E (X) → E (X) to be C -compact. We also show that the sum of two orthogonally additive operators G and T , where G is narrow and T is laterally-to-norm continuous and C -compact, is a narrow operator. In the last part of the article we investigate dominated orthogonally additive operators. In particular we show the narrowness of dominated operators taking values in a Banach sequence space Y or in a separable symmetric operator space C E. [ABSTRACT FROM AUTHOR]

Let X be a smooth Artin stack with properly stable good moduli space X → π X. The purpose of this paper is to prove that a simple geometric criterion can often characterize when the moduli space X is smooth and the morphism π is flat. [ABSTRACT FROM AUTHOR]

A commutative ring with identity is called a zip ring if each of its faithful ideals contains a finitely generated faithful ideal. A natural generalization of this notion is to require every faithful ideal to contain a countably generated faithful ideal. This is what we do in this paper. If a ring has this property, we call it a czip ring. Clearly, every zip ring is a czip ring. We give several characterizations of czip rings, including some in terms of subspaces of the space of minimal prime ideals with the Zariski topology. In rings of continuous functions we characterize the Tychonoff spaces X for which C (X) is a czip ring. This enables us to show that the class of czip rings properly contains that of zip rings. [ABSTRACT FROM AUTHOR]

The paper presents a satisfactory version of the Lie–Trotter product formula in the context of the duality between a quasi-equicontinuos C 0 -semigroup T (t) t ≥ 0 on a locally convex vector space X endowed with some locally convex Hausdorff topology Υ and its adjoint T ∗ (t) t ≥ 0 on the dual space X ∗ endowed with the topology C (X ∗ , X) of uniform convergence on compact subsets of X Υ. An application is given for the transition semigroup of the diffusion associated to the generalized Schrödinger operator on L ∞ (R N , d x). [ABSTRACT FROM AUTHOR]

Consider a connected reductive algebraic group G and a symmetric subgroup K. Let X = K / B K × G / P be a double flag variety of finite type, where B K is a Borel subgroup of K , and P a parabolic subgroup of G. A general argument shows that the orbit space C X / K inherits a natural action of the Hecke algebra H = H (K , B K) of double cosets via convolutions. However, it is a quite different problem to find out the explicit structure of the Hecke module. In this paper, for the double flag variety of type AIII, we determine the explicit action of H on C X / K in a combinatorial way using graphs. As a by-product, we also get the description of the representation of the Weyl group on C X / K as a direct sum of induced representations. [ABSTRACT FROM AUTHOR]

In this paper we establish inclusions and noninclusions between various Hardy type spaces on noncompact Riemannian manifolds M with Ricci curvature bounded from below, positive injectivity radius and spectral gap. Our first main result states that, if L is the positive Laplace–Beltrami operator on M , then the Riesz–Hardy space H R 1 (M) is the isomorphic image of the Goldberg type space h 1 (M) via the map L 1 / 2 (I + L) − 1 / 2 , a fact that is false in R n. Specifically, H R 1 (M) agrees with the Hardy type space X 1 / 2 (M) recently introduced by the first three authors; as a consequence, we prove that H R 1 (M) does not admit an atomic characterisation. Noninclusions are mostly proved in the special case where the manifold is a Damek–Ricci space S. Our second main result states that H R 1 (S) , the heat Hardy space H H 1 (S) and the Poisson–Hardy space H P 1 (S) are mutually distinct spaces, a fact which is in sharp contrast to the Euclidean case, where these three spaces agree. [ABSTRACT FROM AUTHOR]

This article is in line with earlier investigations done in [10–12,14,15,18] and several such works. Here our aim is to introduce and study two new completeness-like properties, namely, Bourbaki quasi-completeness and cofinally Bourbaki quasi-completeness (we use infinite chains instead of finite ones), which strictly lie between compactness and completeness, primarily in the setting of uniform spaces. We use the concept of finite-component covers [19] to define a new type of modification of a uniform space, which plays a crucial role throughout the paper. In Section 2, we relate cBq-completeness to the existing notion of superparacompactness [19]. Another significant and very natural problem we deal with is the topological problem of metrizability of a uniform space using a Bq-complete and a cBq-complete metric. We obtain results similar to the classical Čech theorem about the complete metrizability of a metric space X in terms of its Stone-Čech compactification βX , which are presented in sections 3 and 4 of the article. [ABSTRACT FROM AUTHOR]

In this paper we prove existence and uniqueness of a mild solution to the Young equation d y (t) = A y (t) d t + σ (y (t)) d x (t) , t ∈ [ 0 , T ] , y (0) = ψ. Here, A is an unbounded operator which generates a semigroup of bounded linear operators (S (t)) t ≥ 0 on a Banach space X , x is a real-valued η -Hölder continuous. Our aim is to reduce, in comparison to Gubinelli et al. (2006) and Addona et al. (2022) (see also Deya et al. (2012) and Gubinelli and Tindel, (2010)), the regularity requirement on the initial datum ψ eventually dropping it. The main tool is the definition of a sewing map for a new class of increments which allows the construction of a Young convolution integral in a general interval [ a , b ] ⊂ R when the X α -norm of the function under the integral sign blows up approaching a and X α is an intermediate space between X and D (A). [ABSTRACT FROM AUTHOR]