Lexicographic Effect Algebras

In the paper we investigate a class of effect algebras which can be represented in the form of the lexicographic product \Gamma(H\lex G,(u,0)), where $(H,u)$ is an Abelian unital po-group and $G$ is an Abelian directed po-group. We study algebraic conditions when an effect algebra is of this form. Fixing a unital po-group $(H,u)$, the category of strong $(H,u)$-perfect effect algebra is introduced and it is shown that it is categorically equivalent to the category of directed po-group with interpolation. We show some representation theorems including a subdirect product representation by antilattice lexicographic effect algebras

Geodesic bi-angles and Fourier coefficients of restrictions of eigenfunctions

This article concerns joint asymptotics of Fourier coefficients of restrictions of Laplace eigenfunctions $\phi_j$ of a compact Riemannian manifold to a submanifold $H \subset M$. We fix a number $c \in (0,1)$ and study the asymptotics of the thin sums, $$N^{c} _{\epsilon, H }(\lambda): = \sum_{j, \lambda_j \leq \lambda} \sum_{k: |\mu_k - c \lambda_j | < \epsilon} \left| \int_{H} \phi_j \overline{\psi_k}dV_H \right|^2$$ where $\{\lambda_j\}$ are the eigenvalues of $\sqrt{-\Delta}_M,$ and $\{(\mu_k, \psi_k)\}$ are the eigenvalues, resp. eigenfunctions, of $\sqrt{-\Delta}_H$. The inner sums represent the `jumps' of $N^{c} _{\epsilon, H }(\lambda)$ and reflect the geometry of geodesic c-bi-angles with one leg on $H$ and a second leg on $M$ with the same endpoints and compatible initial tangent vectors $\xi \in S^c_H M, \pi_H \xi \in B^* H$, where $\pi_H \xi$ is the orthogonal projection of $\xi$ to $H$. A c-bi-angle occurs when $\frac{|\pi_H \xi|}{|\xi|} = c$. Smoothed sums in $\mu_k$ are also studied, and give sharp estimates on the jumps. The jumps themselves may jump as $\epsilon$ varies, at certain values of $\epsilon$ related to periodicities in the c-bi-angle geometry. Subspheres of spheres and certain subtori of tori illustrate these jumps. The results refine those of the previous article (arXiv:2011.11571) where the inner sums run over $k: | \frac{\mu_k}{\lambda_j} - c| \leq \epsilon$ and where geodesic bi-angles do not play a role.Comment: 51 pages. Referee's comments incorporated. To appear in Pure and Applied Analysi

Branes And Supergroups

Extending previous work that involved D3-branes ending on a fivebrane with $\theta_{\mathrm{YM}}\not=0$, we consider a similar two-sided problem. This construction, in case the fivebrane is of NS type, is associated to the three-dimensional Chern-Simons theory of a supergroup U$(m|n)$ or OSp$(m|2n)$ rather than an ordinary Lie group as in the one-sided case. By $S$-duality, we deduce a dual magnetic description of the supergroup Chern-Simons theory; a slightly different duality, in the orthosymplectic case, leads to a strong-weak coupling duality between certain supergroup Chern-Simons theories on $\mathbb{R}^3$; and a further $T$-duality leads to a version of Khovanov homology for supergroups. Some cases of these statements are known in the literature. We analyze how these dualities act on line and surface operators.Comment: 143 page

Chaos on Set-Valued Dynamics and Control Sets

The aim of this chapter is threefold. First, we show some advances in complexity dynamics of set-valued discrete systems in connection with the Devaney’s notion of chaos. Secondly, we start to explore some relationships between control sets for the class of linear control systems on Lie groups with chaotic sets. Finally, through several open problems, we invite the readers to give a contribution to this beauty theory

A complex proportional assessment method for group decision making in an interval-valued intuitionistic fuzzy environment

Multi-criteria decision making is an implicational field that concerns with selecting or designing the best scenarios among a finite set of scenarios based on a finite set of criteria. Different methods and techniques for handling this issue have been proposed. Complex proportional assessment is an analytical tool for solving multi-criteria decision making problems. Originally, the COPRAS method has been developed for decision making under a deterministic environment. Since uncertainty is an unavoidable property of decision making due to a lack of knowledge, this paper suggests an extended form of the COPRAS method used for group decision making problems in an uncertain environment where such uncertainty is captured through a generalized form of fuzzy sets - the so called interval valued intuitionistic fuzzy sets. An algorithmic scheme for the COPRAS-IVIF method has been introduced thus examining its application with reference to two numerical examples. It seems that the recommended framework of COPRAS-IVIF can be satisfactorily implemented in decision making problems under ambiguous and ill-defined conditions

A walk in the noncommutative garden

This text is written for the volume of the school/conference "Noncommutative Geometry 2005" held at IPM Tehran. It gives a survey of methods and results in noncommutative geometry, based on a discussion of significant examples of noncommutative spaces in geometry, number theory, and physics. The paper also contains an outline (the ``Tehran program'') of ongoing joint work with Consani on the noncommutative geometry of the adeles class space and its relation to number theoretic questions.Comment: 106 pages, LaTeX, 23 figure

Gaussian Regression Process for Prediction of Compressive Strength of Thermally Activated Geopolymer Mortars

The primary objective of this research is the development of a prediction model of the compressive strength of geopolymer mortars made with fly ash and granular slag which hardened in different curing conditions. Data for the numerical analysis were obtained by experimental research; for this purpose 45 series of geopolymer mortars were made, 9 of which were cured in ambient conditions at a temperature of 22 °С, and the remaining were exposed to thermal activation for a duration of 24 h at the temperatures of 65 °С, 75 °С, 85 °С and 95 °С. Using machine learning, a Gaussian regression method was developed in which the curing temperature and the percentage mass content of fly ash and granular slag were used as input parameters, and the compressive strength as the output. Based on the results of the developed model, it can be concluded that the Gaussian regression process can be used as a reliable regression method for predicting the compressive strength of geopolymer mortars based on fly ash and granular slag

A Sport-Based Intervention to Increase Uptake of Voluntary Medical Male Circumcision Among Adolescent Male Students: Results From the MCUTS 2 Cluster-Randomized Trial in Bulawayo, Zimbabwe.

BACKGROUND: Mathematical models suggest that 570,000 HIV infections could be averted between 2011 and 2025 in Zimbabwe if the country reaches 80% voluntary medical male circumcision (VMMC) coverage among 15- to 49-year-old male subjects. Yet national coverage remains well below this target, and there is a need to evaluate interventions to increase the uptake. METHODS: A cluster-randomized trial was conducted to assess the effectiveness of Make-The-Cut-Plus (MTC+), a single, 60-minute, sport-based intervention to increase VMMC uptake targeting secondary school boys (14-20 years). Twenty-six schools in Bulawayo, Zimbabwe, were randomized to either receive MTC+ at the start (intervention) or end (control) of a 4-month period (March to June 2014). VMMC uptake over these 4 months was measured via probabilistic matching of participants in the trial database (n = 1226 male participants; age, 14-20 years; median age, 16.2 years) and the registers in Bulawayo's 2 free VMMC clinics (n = 5713), using 8 identifying variables. RESULTS: There was strong evidence that the MTC+ intervention increased the odds of VMMC uptake by approximately 2.5 fold (odds ratio = 2.53; 95% confidence interval, 1.21 to 5.30). Restricting to participants who did not report being already circumcised at baseline, MTC+ increased VMMC uptake by 7.6% (12.2% vs 4.6%, odds ratio = 2.65; 95% confidence interval, 1.19 to 5.86). Sensitivity analyses related to the probabilistic matching did not change these findings substantively. The number of participants who would need to be exposed to the demand creation intervention to yield one additional VMMC client was 22.7 (or 13.2 reporting not already being circumcised). This translated to approximately US dollar 49 per additional VMMC client. CONCLUSIONS: The MTC+ intervention was an effective and cost-effective strategy for increasing VMMC uptake among school-going adolescent male subjects in Bulawayo

Effects of oil palm (elais guineensis) fruit extracts on glucose uptake activity of muscle, adipose and liver cells

The effect of oil palm (Elaeis guineensis) fruit aqueous extract (OPF) on glucose uptake activity of three different cell lines was investigated. The cell lines were incubated with different concentrations of OPF to evaluate the stimulatory effect of OPF towards glucose uptake activity of L6 myotubes, 3T3F442A adipocytes and Chang liver cell line. The glucose uptake activities of all tested cells were enhanced in the presence of OPF extract (basal condition). Nevertheless in combination of OPF extract and 100 nM insulin, the glucose uptake activity was only significantly enhanced in L6 myotubes and 3T3F442A adipocytes cell lines. The extracts enhanced the glucose uptake into cells through either insulin-mimetic or insulin-sensitizing property or combination of these two properties. It can be suggested that the OPF extract exerts its antihyperglycemic action partly by mediated glucose uptake into the glucose-responsive disposal cells, muscle, adipose and liver

New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations

This Special Issue puts forward for discussion state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, neutrosophic symmetry, and their applications in the real world. This book leads to the further advancement of the neutrosophic and plithogenic theories of NeutroAlgebra and AntiAlgebra, NeutroGeometry and AntiGeometry, Neutrosophic n-SuperHyperGraph (the most general form of graph of today), Neutrosophic Statistics, Plithogenic Logic as a generalization of MultiVariate Logic, Plithogenic Probability and Plithogenic Statistics as a generalization of MultiVariate Probability and Statistics, respectively, and presents their countless applications in our every-day world