Unitary Type Research Articles

Topological expansion of unitary integrals and maps

We study integrals on the unitary group with respect to the Haar measure. We give a combinatorial interpretation in terms of maps of the asymptotic topological expansion, established previously by Guionnet and Novak. The maps we introduce—the maps of unitary type—satisfy Tutte-like equations. It allows us to show that in the perturbative regime, they describe the different orders of the asymptotic topological expansion. Furthermore, they generalize the monotone Hurwitz numbers.

MIMO Super-Twisting Controller using a passivity-based design

A novel MIMO Super-Twisting Algorithm is proposed in this paper for nonlinear systems with relative degree one, having a time and state-varying uncertain control matrix. The uncertainty is represented by a time and state-varying but unknown left matrix factor. Sufficient conditions for stability with full-matrix control gains are established, in contrast to the usual scalar gains. For this a smooth Lyapunov function, based on a passivity interpretation, is used. Moreover, continuous and homogeneous approximations of the classical discontinuous Super-Twisting algorithm are obtained, using a unified analysis method. Moreover, the proposed Super-Twisting algorithm is of the discontinuous type, in contrast to the usual unitary type.

Moments of Artin–Schreier L-functions

Abstract We compute moments of L-functions associated to the polynomial family of Artin–Schreier covers over $\mathbb{F}_q$, where q is a power of a prime p > 2, when the size of the finite field is fixed and the genus of the family goes to infinity. More specifically, we compute the $k{\text{th}}$ moment for a large range of values of k, depending on the sizes of p and q. We also compute the second moment in absolute value of the polynomial family, obtaining an exact formula with a lower order term, and confirming the unitary symmetry type of the family.

Free Constructions in Hoops via $$\ell $$-Groups

AbstractLattice-ordered abelian groups, or abelian$$\ell $$ ℓ -groups in what follows, are categorically equivalent to two classes of 0-bounded hoops that are relevant in the realm of the equivalent algebraic semantics of many-valued logics: liftings of cancellative hoops and perfect MV-algebras. The former generate the variety of product algebras, and the latter the subvariety of MV-algebras generated by perfect MV-algebras, that we shall call $$\textsf{DLMV}$$ DLMV . In this work we focus on these two varieties and their relation to the structures obtained by forgetting the falsum constant 0, i.e., product hoops and DLW-hoops. As main results, we first show a characterization of the free algebras in these two varieties as particular weak Boolean products; then, we show a construction that freely generates a product algebra from a product hoop and a DLMV-algebra from a DLW-hoop. In other words, we exhibit the free functor from the two algebraic categories of hoops to the corresponding categories of 0-bounded algebras. Finally, we use the results obtained to study projective algebras and unification problems in the two varieties (and the corresponding logics); both varieties are shown to have (strong) unitary unification type, and as a consequence they are structurally and universally complete.

Localization for random quasi-one-dimensional models

In this Review Article, we review the results of Anderson localization for different random families of operators that enter the framework of random quasi-one-dimensional models. We first recall what is Anderson localization from both physical and mathematical points of view. From the Anderson–Bernoulli conjecture in dimension 2, we justify the introduction of quasi-one-dimensional models. Then, we present different types of these models: the Schrödinger type in the discrete and continuous cases, the unitary type, the Dirac type, and the point interaction type. We present tools coming from the study of dynamical systems in dimension one: the transfer matrix formalism, the Lyapunov exponents, and the Furstenberg group. We then prove a criterion of localization for quasi-one-dimensional models of Schrödinger type involving only geometric and algebraic properties of the Furstenberg group. Then, we review results of localization, first for Schrödinger-type models and then for unitary type models. Each time, we reduce the question of localization to the study of the Furstenberg group and show how to use more and more refined algebraic criteria to prove the needed properties of this group. All the presented results for quasi-one-dimensional models of Schrödinger type include the case of Bernoulli randomness.

Personal Fund in the System of Legal Entities

The subject of the research of this article is a personal fund, which is an organizational and legal form of a non-profit organization of a unitary type. The article offers an analysis of the constitutive features of this organizational and legal form, identifies some problems associated with its participation in civil turnover. The mechanisms of personal fund management and its termination are investigated. Options for determining the beneficiary of a personal fund are considered. The assessment of the applied value of the personal fund in view of the factthat the mechanism of legal regulation of the inheritance fund was not effective enough for civil turnover, the legislator developed a more perfect mechanism of legal regulation of the personal fund. It is noted that the main advantage of a personal fund in comparison with a legacy fund is the possibility of its lifetime establishment, monitoring of activities and the possibility of changing the structure of its management during the lifetime of the founder of the personal fund.

The Kudla-Rapoport conjecture at a ramified prime for 𝑈(1,1)

In this paper, we proved a local arithmetic Siegel-Weil formula for a U ( 1 , 1 ) U(1, 1) -Shimura variety at a ramified prime, a.k.a. a Kudla-Rapoport conjecture at a ramified case. The formula needs to be modified from the original Kudla-Rapoport conjecture. In the process, we also give an explicit decomposition of the special divisors of the Rapoport-Zink space of unitary type ( 1 , 1 ) (1, 1) (Krämer model). A key ingredient is to relate the Rapoport-Zink space to the Drinfeld upper plane.

Projectivity and unification in substructural logics of generalized rotations

We develop a unifying approach to study projectivity and unification in substructural logics corresponding to varieties of residuated lattices generated by generalized rotation constructions. These include many interesting varieties especially in the realm of mathematical fuzzy logics. Our main results pertain what we shall call radical-determined varieties of rotations, which include all of the most relevant varieties in this framework. We characterize free algebras in a radical-determined variety V of rotations in terms of weak Boolean products of rotations of free algebras in the variety of radicals, the latter being the intersections of maximal filters of the algebras in V. Then we use such description to study projectivity in these varieties of rotations, characterizing finitely generated projective algebras. Moreover, we show that the strong unitary unification type of a variety of radicals implies the strong unitary type for the generated variety of rotations, which can be used to deduce the decidability of the admissibility of rules. As relevant applications of our general results, we obtain that product logic and nilpotent minimum logic have (strong) unitary unification type.

Adjoint Selmer groups of automorphic Galois representations of unitary type

Let \rho be the p -adic Galois representation attached to a cuspidal, regular algebraic automorphic representation of \operatorname{GL}_n of unitary type. Under very mild hypotheses on \rho , we prove the vanishing of the (Bloch–Kato) adjoint Selmer group of \rho . We obtain definitive results for the adjoint Selmer groups associated to non-CM Hilbert modular forms and elliptic curves over totally real fields.

A feasible approach for automatically differentiable unitary coupled-cluster on quantum computers.

We develop computationally affordable and encoding independent gradient evaluation procedures for unitary coupled-cluster type operators, applicable on quantum computers. We show that, within our framework, the gradient of an expectation value with respect to a parameterized n-fold fermionic excitation can be evaluated by four expectation values of similar form and size, whereas most standard approaches, based on the direct application of the parameter-shift-rule, come with an associated cost of expectation values. For real wavefunctions, this cost can be further reduced to two expectation values. Our strategies are implemented within the open-source package Tequila and allow blackboard style construction of differentiable objective functions. We illustrate initial applications through extended adaptive approaches for electronic ground and excited states.

Automorphy lifting for residually reducible -adic Galois representations, II

We revisit the paper [Automorphy lifting for residually reducible$l$-adic Galois representations, J. Amer. Math. Soc. 28 (2015), 785–870] by the third author. We prove new automorphy lifting theorems for residually reducible Galois representations of unitary type in which the residual representation is permitted to have an arbitrary number of irreducible constituents.

Compositional relationship between the source-to-sink segments and their sedimentary response to diverse geomorphology types in the intrabasinal lower uplift of continental basins

Investigating on new method for Source-to-Sink study by integrating modern system and subsurface interpretation, establishment of the quantitative coupling model from source to sink, and form industrial application standard have long been the research trends of Source-to-Sink system in continental basins. Here the symmetrical and asymmetrical conceptual source-to-sink coupling models (i.e., Symmetrical Dumbbell Type and Asymmetrical Dumbbell Type) are proposed to respond to diverse geomorphology types (i.e., convergent and unitary incised type) based on the morphological and digital proportion between catchment-drainage unit of upstream and sediment-fan of downstream, then summarize and extract the two models by contrasting a modern source-to-sink system of Hovd Central Uplift in northwestern Mongolia as well as an ancient source-to-sink system of Huizhou-Lufeng Lower Uplift in Pearl River Mouth Basin, South China Sea. In the practical study, the satellite remote sensing and Google geological map are used to deconstruct the modern case and combine the Google-topographic-map, well log data, core data and seismic-geomorphology analysis to dissect the ancient case analogously. This paper mainly discusses morphological proportional ranges of catchment acreage (Asource) and sediment fan acreage (Ssink), the relativity between topographic gradient (Gsource) and the source ratio (Rsource=AsourceAsource+Ssink), and the physical properties of sedimentary sand-body associated with diverse geomorphologic types in continental lacustrine basins. Therefrom, it is concluded that the proportion (P=Asource:Ssink) between catchment-drainage segment of source area (Asource) and sediment-fan of depositional sink (Ssink) is over 1:1 in Symmetrical Dumbbell Type source-to-sink coupling model, which is commonly between 1:1.1 and 1:1.6; However, it is below 1:1 in Asymmetrical Dumbbell Type source-to-sink coupling model, which is generally between 1:0.6 and 1:0.9; and there is an evident negative correlation between topographic gradient (Gsource) and the source ratio (Rsource). Finally, these results reveal that the reservoir formed by Symmetrical Dumbbell Type source-to-sink coupling model performs much more superiority. In summary, the two coupling models have not only supplied a new insight into the research on sandy-sediments transport and distribution, but also defined the directions for better finding favourable sand bodies (reservoir) when exploring oil and gas.

On groups with a strongly embedded unitary subgroup

The proper subgroup $B$ of the group $G$ is called {\it strongly embedded}, if $2\in\pi(B)$ and $2\notin\pi(B \cap B^g)$ for any element $g \in G \setminus B $ and, therefore, $ N_G(X) \leq B$ for any 2-subgroup $ X \leq B $. An element $a$ of a group $G$ is called {\it finite} if for all $ g\in G $ the subgroups $ \langle a, a^g \rangle $ are finite. In the paper, it is proved that the group with finite element of order $4$ and strongly embedded subgroup isomorphic to the Borel subgroup of $U_3(Q)$ over a locally finite field $Q$ of characteristic $2$ is locally finite and isomorphic to the group $U_3(Q)$. Keywords: A strongly embedded subgroup of a unitary type, subgroups of Borel, Cartan, involution, finite element.

T3SEpp: an Integrated Prediction Pipeline for Bacterial Type III Secreted Effectors.

Many Gram-negative bacteria infect hosts and cause diseases by translocating a variety of type III secreted effectors (T3SEs) into the host cell cytoplasm. However, despite a dramatic increase in the number of available whole-genome sequences, it remains challenging for accurate prediction of T3SEs. Traditional prediction models have focused on atypical sequence features buried in the N-terminal peptides of T3SEs, but unfortunately, these models have had high false-positive rates. In this research, we integrated promoter information along with characteristic protein features for signal regions, chaperone-binding domains, and effector domains for T3SE prediction. Machine learning algorithms, including deep learning, were adopted to predict the atypical features mainly buried in signal sequences of T3SEs, followed by development of a voting-based ensemble model integrating the individual prediction results. We assembled this into a unified T3SE prediction pipeline, T3SEpp, which integrated the results of individual modules, resulting in high accuracy (i.e., ∼0.94) and >1-fold reduction in the false-positive rate compared to that of state-of-the-art software tools. The T3SEpp pipeline and sequence features observed here will facilitate the accurate identification of new T3SEs, with numerous benefits for future studies on host-pathogen interactions.IMPORTANCE Type III secreted effector (T3SE) prediction remains a big computational challenge. In practical applications, current software tools often suffer problems of high false-positive rates. One of the causal factors could be the relatively unitary type of biological features used for the design and training of the models. In this research, we made a comprehensive survey on the sequence-based features of T3SEs, including signal sequences, chaperone-binding domains, effector domains, and transcription factor binding promoter sites, and assembled a unified prediction pipeline integrating multi-aspect biological features within homology-based and multiple machine learning models. To our knowledge, we have compiled the most comprehensive biological sequence feature analysis for T3SEs in this research. The T3SEpp pipeline integrating the variety of features and assembling different models showed high accuracy, which should facilitate more accurate identification of T3SEs in new and existing bacterial whole-genome sequences.

Non-Entrepreneurial Legal Entity: The Theoretical And Legal Analysis Of The Concept And Characteristics

The article is devoted to the theoretical and legal analysis of issues related to the range of problems connected with development of such legal model as ‘nonentrepreneurial legal entity’. In the scientific work the author makes an analysis of those concepts which are submitted by the leading Ukrainian scholars and concern the formation of civil-law terminology in general and that is applied to the nonentrepreneurial legal entities, in particular.
 The author has concluded that it is expedient to apply the set of criteria during formation of the non-entrepreneurial legal entity. The article gives the definition of non-entrepreneurial legal entity in the narrow and broad meanings.
 It is proved that a non-business entity should be singled out as a separate category according to the non-distribution of profit (income) rather than to the specifics of its business activity. The author demonstrates the feasibility to change classification criteria and levels while classifying the legal entities and on the mentioned ground she has singled out: 1) procedure for establishment of the legal entity; 2) structure of the legal entity as a criterion of the second classification level; 3) specific character of the profit distribution as a criterion of the third level of classification. It is based on the argument that non-business entities are an independent group of the legal entities, which is divided into subgroups: the non-business entities of corporate type and the non-business entities of unitary type. Each subgroup of the non-business legal entity distinguishes several legal forms within of which specific types of non-business entities are allocated.
 The author presents one’s own definition of the non-entrepreneurial legal entity, as a legal entity of public or private law, whether of corporate or unitary type, which is specially established in the different areas of social life and endowed with a special legal capacity.
 The non-entrepreneurial legal entity shall be entitled to carry out activities with a view to profit but it doesn’t distribute it among participants (members).

Assessment of physical activity status among pregnant women in southwestern China

Abstract Objective To assess the patterns and intensities of physical activity among pregnant women in southwestern China, which help us create a fitness regimen based on the 2002 American College of Obstetricians and Gynecologists (ACOG) guidelines for exercise during pregnancy. Methods A cross-sectional study was performed to recruit pregnant women at a prenatal checking visit clinic with the self-administered Chinese version of Pregnancy Physical Activity Questionnaire (PPAQ). Results A total of 1179 Chinese pregnant women were enrolled, of whom 92.60% were classified as not meeting the ACOG guidelines. By intensity, 47.36% of the score was attributed to light-intensity activities (1.5 to <3.0 metabolic equivalent [MET]) in the first trimester; the other 2 trimesters were similar. By patterns, about 45.15% of the score was attributed to inactivity. More than 82.35% of enrolled pregnant women regarded slowly walking as the most common type of exercise during pregnancy. Conclusions This study represents a group of Chinese women who maintained an inactive lifestyle, including low-intensity activities and unitary type of exercises during their pregnancy. Health-care providers are advised to provide appropriate physical activity guidelines to pregnant women. Development of MET-hours/week recommendations is warranted to promote greater physical activity during pregnancy.

Spatial characteristics analysis of Eaves Gallery along the street in China: take Hubei, Bashu, Jiangzhe areas as examples

ABSTRACTThe Eaves Gallery (EG) along the street as a form of Chinese traditional dwelling was special architecture form for preventing pedestrians from rains and snows while walking through or shopping which has played important roles in the ancient commercial activities. In the past, the studies about EG focused on architectural history, style, evolution in the separated specific local area. It helped the promotion of social attention to EG for protection and renewal. However, the protection and renewal conditions of EG are different in various regions of China. Few studies have done to compare and overview the characteristics of EG in these various regions. In this study, typical EG along the streets in Hubei, Bashu, Jiangzhe along Yangtze River regions from east to west of China were taken as case studies and are explicated based on the comparison and analyzing field distribution mode, space combination, spatial scale, and function. Thus, the spatial functional characteristics of EG in these three regions are divided into unitary type, conversion type and mixed type. The outcome will serve as a comparative basis for the existential form and spatial characteristics of extant traditional EG accompanied by optimum protection and renewal policy discussion in the future.

N-level densities for twisted cubic Dirichlet L-functions

For any given cuspidal representation π of GLm(AQ), we consider the family of automorphic L-functions L(s,π×χ) twisted by cubic Dirichlet characters. We compute the n-level density for this family and confirm that it agrees with unitary type U.

On two arithmetic theta lifts

Our aim is to clarify the relationship between Kudla’s and Bruinier’s Green functions attached to special cycles on Shimura varieties of orthogonal and unitary type, which play a key role in the arithmetic geometry of these cycles in the context of Kudla’s program. In particular, we show that the generating series obtained by taking the differences of the two families of Green functions is a non-holomorphic modular form and has trivial (cuspidal) holomorphic projection. Along the way, we construct a section of the Maaß lowering operator for moderate growth forms valued in the Weil representation using a regularized theta lift, which may be of independent interest, as it in particular has applications to mock modular forms. We also consider arithmetic-geometric applications to integral models of$U(n,1)$Shimura varieties. Each family of Green functions gives rise to a formal arithmetic theta function, valued in an arithmetic Chow group, that is conjectured to be modular; our main result is the modularity of the difference of the two arithmetic theta functions. Finally, we relate the arithmetic heights of the special cycles to special derivatives of Eisenstein series, as predicted by Kudla’s conjecture, and describe a refinement of a theorem of Bruinier, Howard and Yang on arithmetic intersections against CM points.

Quantum Markov processes: From attractor structure to explicit forms of asymptotic states

Markov processes play an important role in physics and the theory of open systems in particular. In this paper we study the asymptotic evolution of trace-nonincreasing homogenous quantum Markov processes (both types, discrete quantum Markov chains and continues quantum dynamical semigroups) equipped with a so-called strictly positive T -state in the Schrodinger and the Heisenberg picture. We derive a fundamental theorem specifying the structure of the asymptotic and uncover a rich set of transformations between attractors of quantum Markov processes in both pictures. Moreover, we generalize the structure theorem derived for quantum Markov chains to quantum dynamical semigroups showing how the internal structure of generators of quantum Markov processes determines attractors in both pictures. Based on these results we provide two characterizations of all asymptotic and stationary states, both strongly reminding in form the well-known Gibbs states of statistical mechanics. We prove that the dynamics within the asymptotic space is of unitary type, i.e. quantum Markov processes preserve a certain scalar product of operators from the asymptotic space, but there is no corresponding unitary evolution on the original Hilbert space of pure states. Finally simple examples illustrating the derived theory are given.