Narrow Results

In the Ising model at zero external field with ferromagnetic first neighbors interaction the Gibbs measure is investigated using the group properties of the contours configurations. Correlation inequalities expressing positive dependence among groups and comparison among groups and cosets are used. An improved version of the Griffiths' inequalities is proved for the Gibbs measure conditioned to a subgroup. Examples of positive and negative correlations among the spin variables are proved under conditioning to a contour or to a separation line.

This paper addresses the question of simultaneously solving a set of equations in one variable over torsion-free groups.

We construct a finitely presented group with coNP-complete word problem, and a finitely generated simple group with coNP-complete word problem. These groups are represented as Thompson groups, hence as partial transformation groups of strings. The proof provides a simulation of combinational circuits by elements of the Thompson–Higman group G_3,1.

We show that the probability of generating an iterated wreath product of non-abelian finite simple groups converges to 1 as the order of the first simple group tends to infinity provided the wreath products are constructed with transitive and faithful actions. This has the consequence that the profinite group which is the inverse limit of these iterated wreath products is positively finitely generated.

The connection between classical model theoretical types (MT-types) and logically-geometrical types (LG-types) introduced by B. Plotkin is considered. It is proved that MT-types of two $n$-tuples in two universal algebras coincide if and only if their LG-types coincide. Two problems set by B. Plotkin are considered: (1) let two tuples in an algebra have the same type, does it imply that they are connected by an automorphism of this algebra? and (2) let two algebras have the same type, does it imply that they are isomorphic? Some varieties of universal algebras are considered having in view these problems. In particular, it is proved that if a variety is hopfian or co-hopfian, then finitely generated free algebras of such a variety are completely determined by their type.

We present modeling strategies that describe the motion and interaction of groups of pedestrians in obscured spaces. We start off with an approach based on balance equations in terms of measures and then we exploit the descriptive power of a probabilistic cellular automaton model.

Based on a variation of the simple symmetric random walk on the square lattice, we test the interplay between population size and an interpersonal attraction parameter for the evacuation of confined and darkened spaces. We argue that information overload and coordination costs associated with information processing in small groups are two key processes that influence the evacuation rate. Our results show that substantial computational resources are necessary to compensate for incomplete information — the more individuals in (information processing) groups the higher the exit rate for low population size. For simple social systems, it is likely that the individual representations are not redundant and large group sizes ensure that this non-redundant information is actually available to a substantial number of individuals. For complex social systems, information redundancy makes information evaluation and transfer inefficient and, as such, group size becomes a drawback rather than a benefit. The effect of group sizes on outgoing fluxes, evacuation times and wall effects is carefully studied with a Monte Carlo framework accounting also for the presence of an internal obstacle.

The evacuation of human crowds consisting of several groups in complex venues is studied, in this paper, by the kinetic theory of active particles. We consider a complex venue that consists of several chambers which are separated by interior walls and doors, for which the geometrical effects may come from the walls both on the boundary and inside the domain, the exits, and the doors connecting the chambers. The geometrical properties are incorporated in the geometrical preferred direction, which is specified such that an individual can avoid the wall and approach the exit through the evacuation vector. The notion of group is corresponding to the concept of functional subsystem in the mathematical theory of active particles. In the present framework of several groups, the rules of interactions can be specified for both the interactions among the same group and the interactions between different groups. Furthermore, the motility is assigned for each group, which serves as the average activity of a group. Some interesting features and phenomena are shown in the numerical tests of the evacuation of a crowd with one, two or three groups.

Behaviour analysis loop is largely performed on virtual product model before its physical manufacturing. The last avoids high expenses in terms of money and time spent on intermediate manufacturing. It is gainful from the reality to the virtuality but the process could be further optimized especially during the product behaviour optimization phase. This process involves repetition of four main processing steps: CAD design and modification, mesh creation, Finite Element (FE) model generation with the association of physical and geometric data, FE Analysis. The product behaviour analysis loop is performed on the first design solution as well as on the numerous successive product optimization loops. Each design solution evaluation necessitates the same time as required for the first product design that is particularly crucial in the context of maintenance.

In this paper we propose a new framework for CAD-less product optimisation through FE analysis which reduces the model preparation activities traditionally required for FE model creation. More concretely, the idea is to directly operate on the firstly created FE mesh, enriched with physical/geometric semantics, to perform the product modifications required to achieve its optimised version.

In order to accomplish the proposed CAD-less FE analysis framework, modification operators acting on both the mesh geometry and the associated semantics need to be devised. In this paper we discuss the underlying concepts and present possible components for the development of such operators. A high-level operator specification is proposed according to a modular structure that allows an easy realisation of different mesh modification operators. Here, two instances of this high-level operator are described: the planar cracking and the drilling. The realised prototypes validated on industrial FE models show clearly the feasibility of this approach.

Dependent variables used by Kim, Jung and Kim (2005) to assess the effect of the ownership structure of Korean chaebols on internal funds allocations are a priori misspecified in the context of their research, as they were designed to be applied when studying diversified firms and not groups consisting of legally independent entities. The conditions under which this misspecification has no effect on their conclusions are discussed. Re-analyzing their data with a more appropriate internal funds allocation variable leaves their conclusion on the presence of tunnelling effects intact, though it paints a partly different picture of internal allocations as such.

In this paper we explicitly determine all indicators for groups isomorphic to the semidirect product of two cyclic groups by an automorphism of prime order, as well as the generalized quaternion groups. We then compute the indicators for the Drinfel'd doubles of these groups. This first family of groups include the dihedral groups, the non-abelian groups of order pq, and the semidihedral groups. We find that the indicators are all integers, with negative integers being possible in the first family only under certain specific conditions.

Let G be a group, t an element distinct from G and r(t)= g₁t^l₁ ⋯ g_kt^l_k∈ G ∗ 〈t 〉, where each g_i is an element of G of order greater than 2 and the l_i are non-zero integers such that l₁+l₂+ ⋯ +l_k≠ 0 and |l_i| ≠ |l_j| for i ≠ j. It is known that if k≤ 2, then the natural map from G to the one-relator product 〈G,t | r(t)〉 is injective. In this paper, we prove that the same holds for all k ∉ {4, 5}.

With the rapid growth of the rural tourism industry, traditional tourism recommendation technologies can no longer meet the necessary requirements. To address the issue of rural tourist attraction recommendations, a rural tourist attraction recommendation model is constructed based on a multi-feature fusion graph neural network. First, construct a feature map based on the relationship between tourists’ preferences and tourist attractions, and incorporate the attention mechanism to enhance the model’s learning capabilities. Second, utilize a two-part graph model to extract positive and negative preference features of tourists, and a conversation graph model to extract tourists’ transfer preference features. Finally, various features are utilized to generate suggested content by computing scores for tourists’ travel preferences. To address the problem of recommending tourist groups, suitable features for random group matching are collected and the cosine function is employed to identify users with similar random group features. Finally, the multi-features are merged, and the tourists’ interest preferences are scored to arrive at content recommendations. In the experiment on individualized attraction recommendations, data from the Chengdu area were used to test the proposed model. The accuracy of the model’s recommendations was 0.822 for five recommendations which outperformed the other models. In the experiment for group-based attraction recommendations, this experiment tested the Chengdu dataset. The proposed model achieved the highest accuracy of 0.972 when the group size was 70, outperforming the other two models. Additionally, with regards to different numbers of recommendations, the proposed model’s accuracy was 0.5241, which was the best performance among the three models when the number of recommendations was set to five. The proposed recommendation model performs optimally in suggesting tourist attractions and meets the needs of rural tourism. The research content provides crucial technical references for tourist traveling and rural tourism development.

In 2019, Öztürk et al. [Gamma semigroups on weak nearness approximation spaces, Journal of the International Mathematical Virtual Institute9 (2019) 53–72] defined the first algebraic structure on weak nearness approximation spaces which is the gamma semigroup. After this study, the view on the nearness of algebraic structures has completely changed. This view was first expressed in a previous study in 2021 [M. A. Öztürk, Nearness $d$-algebras, Journal of Algebraic Hyperstructures and Logical Algebras2 (2021) 73–84]. Our aim is to give the concept of modulo in the nearness group $G$ as in the nearness group $(Z,+)$, where $Z$ is the set of integers. Afterward, based on the concept of modulo in the nearness group $G$, the nearness cosets of the nearness group $G$ are constructed and its basic properties are examined. Lastly, it is seen that Lagrange theorem is not valid for the nearness subgroups as compared to the usual subgroups.

We give an explicit finite presentation of a group normally generated by SL_∞(ℤ). As a consequence, such a group cannot act on e.g. a finite dimensional contractible manifold or on a compact manifold.

Uniform spanning trees on finite graphs and their analogues on infinite graphs are a well-studied area. On a Cayley graph of a group, we show that they are related to the first ℓ²-Betti number of the group. Our main aim, however, is to present the basic elements of a higher-dimensional analogue on finite and infinite CW-complexes, which relate to the higher ℓ²-Betti numbers. One consequence is a uniform isoperimetric inequality extending work of Lyons, Pichot, and Vassout. We also present an enumeration similar to recent work of Duval, Klivans and Martin.

Let M be a closed connected manifold and let D be an elliptic operator on M. Let G be a discrete countable group and let be a principal G-bundle. Connes and Moscovici showed that this data defines an analytic index ind_ℓ¹(G)(D) ∈ K₀(ℓ¹(G)). If B is a unital tracial C*-algebra, we give a formula for the trace of the image of ind_ℓ¹(G)(D) in K₀(B) under the map induced by a quasi-representation of G in B. As an application, we reprove and generalize a formula of Exel and Loring to surface groups.

The algorithmic unsolvability of the conjugacy problem for finitely presented groups was demonstrated by Novikov in the early 1950s. Various simplifications and alternative proofs were found by later researchers and further questions raised. Recent work by Borovik, Myasnikov and Remeslennikov has considered the question of what proportion of the number of elements of a group (obtained by standard constructions) falls into the realm of unsolvability. In this paper we provide a straightforward construction, as a Britton tower, of a finitely presented group with solvable word problem but unsolvable conjugacy problem of any r.e. (recursively enumerable) Turing degree a. The question of whether two elements are conjugate is bounded truth-table reducible to the question of whether the elements are both conjugate to a single generator of the group. We also define computable normal forms, based on the method of Bokut', that are suitable for the conjugacy problem. We consider (ordered) pairs of normal words U, V for the conjugacy problem whose lengths add to l and show that the proportion of such pairs for which conjugacy is undecidable (in the case a ≠ 0) is strictly less than l²/(2λ - 1)^l where λ > 4.

The construction is based on modular machines, introduced by Aanderaa and Cohen. For the purposes of this construction it was helpful to extend the notion of configuration to include pairs of m-adic integers. The notion of computation step was also extended and is referred to as s-fold computation where s ∈ ℤ (the usual notion coresponds to s = 1). If gcd(m, s) = 1 then determinism is preserved, i.e., if the modular machine is deterministic then it remains so under the extended notion. Furthermore there is a simple correspondence between s-fold and standard computation in this case. Otherwise computation is non-deterministic and there does not seem to be any straightforward correspondence between s-fold and standard computation.

In this paper, we study properties of the endomorphism monoids of strong semilattices of groups. In Sec. 2, several properties for endomorphism monoids of finite semilattices are investigated. In Sec. 3, we collect some results on endomorphism monoids of strong semilattices of groups, i.e. Clifford semigroups.

The purpose of this paper is to describe the nearness homomorphisms and the canonical nearness epimorphism of the nearness groups and to investigate their basic properties. It is also to form the substructure to give the nearness isomorphism theorems of the nearness groups.

We prove some basic results on left groups and their homomorphisms and characterize congruences and homomorphisms on these semigroups. Finally we investigate some properties of the endomorphism monoid of a left group.