Irreducible Representations Research Articles

The Use of Uncertainty Reduction Theory in Communication

Based on references that are mainly published in recent years, this paper focuses on the application of uncertainty reduction theory (URT) in communication science in recent years. After explaining concepts that are related with URT, this paper reflects on the possible application of URT in different scenarios proposed by previous researchers, and therefore provides guidelines of reducing uncertainty--either passive, active or interactive strategies. It reveals certain realms that need to be studied on, including proposing generalizable researches that helps unify the theory, updating research data on specific contexts using URT, including more types of communication in the theory, and improving the modified URT framework in various communication environments. By doing so, it attempts to conclude current research trends in this field, inspiring future researchers to dive deeper into where research gaps exist. This article successfully extended the boarder of the objective of uncertainty as well as the scenarios that are explained by URT.

Spin degrees of freedom incorporated in conformal group: Introduction of an intrinsic momentum operator

Considering spin degrees of freedom incorporated in the conformal generators, we introduce an intrinsic momentum operator \pi_\muπμ, which is feasible for the Bhabha wave equation. If a physical state \psi_{ph}ψph for spin s is annihilated by the \pi_\muπμ, the degree of \psi_{ph}ψph, deg \psi_{ph}ψph, should equal twice the spin degrees of freedom, 2 ( 2 s + 1)2(2s+1) for a massive particle, where the multiplicity 22 indicates the chirality. The relation deg \psi_{ph}ψph = 2(2s+1) holds in the representation R_5R5 (s,s), irreducible representation of the Lorentz group in five dimensions.

Bruhat-Tits buildings, representations of p-adic groups and Langlands correspondence

The Bruhat-Tits theory is a key ingredient in the construction of irreducible smooth representations of p-adic reductive groups. We describe generalizations to arbitrary such representations of several results recently obtained in the case of supercuspidal representations, in particular regarding the local Langlands correspondence and the internal structure of the L-packets.We prove that the enhanced L-parameters with semisimple cuspidal support are those which are obtained via the (ordinary) Springer correspondence.Let G be a connected reductive group over a non-archimedean field F of residual characteristic p. In the case where G splits over a tamely ramified extension of F and p does not divide the order of the Weyl group of G, we show that the enhanced L-parameters with semisimple cuspidal support correspond to irreducible smooth representations of G(F) with non-singular supercuspidal support via the local Langlands correspondence constructed by Kaletha, under the assumption that the latter satisfies certain expected properties of functorial nature. As a consequence, we obtain that every compound L-packet of G(F) contains at least one representation with non-singular supercuspidal support.

Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applications

We give a brief review on recent developments of \mathbb{Z}_2^nℤ2n-graded symmetry in physics in which hidden \mathbb{Z}_2^nℤ2n-graded symmetries and \mathbb{Z}_2^nℤ2n-graded extensions of known systems are discussed. This elucidates physical relevance of the \mathbb{Z}_2^nℤ2n-graded algebras. As an example of physically interesting algebra, we take \mathbb{Z}_2^2ℤ22-graded supersymmetry (SUSY) algebras and consider their irreducible representations (irreps). A list of irreps for N = 1, 2N=1,2 algebras is presented and as an application of the irreps, \mathbb{Z}_2^2ℤ22-graded SUSY classical actions are constructed.

Generalized Heisenberg-Weyl groups and Hermite functions

A generalisation of Euclidean and pseudo-Euclidean groups is presented, where the Weyl-Heisenberg groups, well known in quantum mechanics, are involved. A new family of groups is obtained including all the above-mentioned groups as subgroups. Symmetries, like self-similarity and invariance with respect to the orientation of the axes, are properly included in the structure of this new family of groups. Generalized Hermite functions on multidimensional spaces, which serve as orthogonal bases of Hilbert spaces supporting unitary irreducible representations of these new groups, are introduced.

First-principles investigation of the magnetoelectric properties of Ba7Mn4O15

Type-II multiferroics, in which the magnetic order breaks inversion symmetry, are appealing for both fundamental and applied research due their intrinsic coupling between magnetic and electrical orders. Using first-principles calculations we study the ground state magnetic behaviour of Ba7Mn4O15 which has been classified as a type-II multiferroic in recent experiments. Our constrained moment calculations with the proposed experimental magnetic structure shows the spontaneous emergence of a polar mode giving rise to an electrical polarisation comparable to other known type-II multiferroics. When the constraints on the magnetic moments are removed, the spins self-consistently relax into a canted antiferromagnetic ground state configuration where two magnetic modes transforming as distinct irreducible representations coexist. While the dominant magnetic mode matches well with the previous experimental observations, the second mode is found to possess a different character resulting in a non-polar ground state. Interestingly, the non-polar magnetic ground state exhibits a significantly strong linear magnetoelectric (ME) coupling comparable to the well-known multiferroic BiFeO3, suggesting strategies to design new linear MEs.

Modelling and Prediction of Fe/MWCNT Nanocomposites for Hexavalent Chromium Reduction

Chromium (Cr) is a heavy metal pollutant prevalent in freshwater resources. Current investigations into Cr(VI) removal materials primarily involve multi-component materials. Among them, iron nanoparticles and multi-walled carbon nanotubes (MWCNTs) have exhibited great promise of removal capabilities. However, determining the optimal component ratio(s) experimentally still requires a substantial amount of effort. This paper presents a novel, model-based approach which can lessen the burden by predicting the performance of new materials. The model is based on reaction kinetics equations and derives its input parameters from the size and surface area characterisations of the components, individual components removal performance, and their mixture performance at one specific component ratio. The model is validated against experimental results for Fe/MWCNT mixtures at six ratios. The root mean square error of our model is 3.95 mg/g, which is less than 3% of the total adsorption capacity, indicating that the model is reliable. The model can be used to identify the optimal component ratios of the Fe-MWCNT composite and to reveal the relationship between performance and time. To the best of our knowledge, this is the first semi-empirical model that can predict the adsorption capacity of a composite material for heavy metals. The model is founded on the generic reduction theory of adsorption, and model parameters are not tied specifically to Fe/MWCNT. Thus, it can be used for predicting the adsorption reduction properties of other multiphase materials to speed up the new material design process.

Investigation of lithium-ion battery nonlinear degradation by experiments and model-based simulation

Understanding the lithium-ion battery (LIB) nonlinear degradation is essential for battery full-lifespan usage and management. In this study, LIBs are cycled under conditions of low-temperature and high-current charging respectively. By designing a multi-battery parallel aging experiment, the evolution process and changing regulation of lithium ions (Li-ions) loss are quantified. The amount of irreversible lithium loss caused by two side reactions, i.e., the side reaction of SEI film growth and irreversible lithium plating, within the full lifespan of LIBs is measured and analyzed, which reveals that irreversible lithium plating is the dominant reason causing the battery nonlinear degradation. With the quantitative results above, an electrochemical aging coupled model is established, which agrees well with the experimental nonlinear aging. Furthermore, a simulation of the battery secondary capacity diving is conducted, and the formation of the nonlinear aging mechanism is revealed. A porosity reduction theory is proposed, in which the capacity diving of the battery is caused by the exponential growth of irreversible lithium plating, while the exponential growth phenomenon is due to the positive feedback loop formed by the porosity reduction of the negative electrode and the irreversible lithium plating.

Reflection on Lowering the Minimum Age of Criminal Responsibility

The amendment to the Criminal Law (Xi) lowered the lower limit of the age of criminal responsibility for minors by introducing theories such as flexibility theory and reduction theory. However, regarding the issue of special cruel means and bad circumstances, there is no specific provision and explanation in the new age of juvenile criminal responsibility in China, which leads to the expansion of the discretion of the legislature and the judiciary. In order to reduce the juvenile crime rate and punish and prevent juvenile delinquents, we should revise the juvenile delinquents in law to fill up the deficiency of compulsory education in prison, perfect the system of special education correction and establish the system of compulsory parental education. Adopting welfare protection has the function of education and correction for juvenile delinquents who are below the lower limit of the age of criminal responsibility.

Determinants and Prevalence of Drug Abuse by Gender in the Selected Competitive Sports at the Universities in Kenya

Purpose: The main objective of this study was to identify the determinants and prevalence of drug abuse by gender in selected competitive sports at the universities in Kenya.
 Methodology: The study used a mixed methods research design with an intention to capture and utilise both qualitative andquantitative data. The study sample comprised 300 respondents. Out of the 300 students, 173(57.7%) were male and 127 (42.3%) were female players derived from six selected competitive sports at the universities in Kenya.The selected sports were badminton, tennis, basketball, volleyball, soccer and rugby. Stratified sampling followed by simple random sampling was used to select 10 universities proportionately (4 private and 6 public), the method was the most appropriate to capture universities with women rugby in addition to the five other selected sports. The study sought to investigate the prevalence of drug abuse due to factors such as psychosocial, medicinal and competition. SPSS computer version 20 was used to process data. The data was presented inform of Tables.
 Findings: The study found that more male players than females abused drugs, with majority being rugby players. Findings indicated that there were more males than females abusing drugs at approximately 89% and 11% respectively. It was concluded that more male than female athletes engaging in sports in universities in Kenya, abuse drugs. This could be attributed to the assumption that males tend to experiment more on most things than do their female counterparts.
 Unique Contribution to Theory, Practice and Policy: The Social Learning Theory, Self Determination Theory and Harm Reduction Theory may be used to anchor future studies. It was recommended that various stakeholders that include the university management, NACADA and the security apparatus work together with an aim to sensitize and curb drug abuse menace among university athletes, general students’ community and the entire community bordering the universities.

Explicit form of Laplace-Beltrami operator on SO(3) in the view of Fourier analysis

Fourier analysis plays a central role in the modern physics, engineering, and mathematics itself. In the field of differential geometry, a Lie group G gives a symmetric structure, and one may apply the Fourier analysis by means of matrix-valued irreducible representations. Even though the entries of these irreducible representations are already shown to be the eigenfunctions of the Laplace-Beltrami operator, it is still desirable to consider a concrete example where both the operator and the irreducible representations can be computed explicitly. This study gives an explicit form of the Laplace-Beltrami operator on SO(3) using direct computations and show also that each entry of the irreducible representations o_n^ij is indeed an eigenfunction of this operator. Therefore, one can also find the application of the Fourier Analysis on differential equations, in this study Poissons equation as an example, using the Laplace-Beltrami operator as the corresponding differential operator. Overall, these results shed light on guiding further exploration of Fourier analysis.

Hecke algebras for p-adic reductive groups and Local Langlands Correspondences for Bernstein blocks

We study the endomorphism algebras attached to Bernstein components of reductive p-adic groups and construct a local Langlands correspondence with the appropriate set of enhanced L-parameters, using certain “desiderata” properties for the LLC for supercuspidal representations of proper Levi subgroups. We give several applications of our LLC to various reductive groups with Bernstein blocks cuspidally supported on general linear groups.In particular, for Levi subgroups of maximal parabolic subgroups of the split exceptional group G2, we compute the explicit weight functions for the corresponding Hecke algebras, and show that they satisfy a conjecture of Lusztig's. Some results from §4 are used by the same authors to construct a full local Langlands correspondence in [9]. Moreover, we prove a “reduction to depth-zero” result for regular Bernstein blocks (i.e., blocks for which the supercuspidal support of each irreducible representation is regular).

Spin(8,C)-Higgs pairs over a compact Riemann surface

Abstract Let X X be a compact Riemann surface of genus g ≥ 2 g\ge 2 , G G be a semisimple complex Lie group and ρ : G → GL ( V ) \rho :G\to {\rm{GL}}\left(V) be a complex representation of G G . Given a principal G G -bundle E E over X X , a vector bundle E ( V ) E\left(V) whose typical fiber is a copy of V V is induced. A ( G , ρ ) \left(G,\rho ) -Higgs pair is a pair ( E , φ ) \left(E,\varphi ) , where E E is a principal G G -bundle over X X and φ \varphi is a holomorphic global section of E ( V ) ⊗ L E\left(V)\otimes L , L L being a fixed line bundle over X X . In this work, Higgs pairs of this type are considered for G = Spin ( 8 , C ) G={\rm{Spin}}\left(8,{\mathbb{C}}) and the three irreducible eight-dimensional complex representations which Spin ( 8 , C ) {\rm{Spin}}\left(8,{\mathbb{C}}) admits. In particular, the reduced notions of stability, semistability, and polystability for these specific Higgs pairs are given, and it is proved that the corresponding moduli spaces are isomorphic, and a precise expression for the stable and not simple Higgs pairs associated with one of the three announced representations of Spin ( 8 , C ) {\rm{Spin}}\left(8,{\mathbb{C}}) is described.

Finite groups with many p-regular conjugacy classes

Let G be a finite group and let p be a prime. In this paper, we study the structure of finite groups with a large number of p-regular conjugacy classes or, equivalently, a large number of irreducible p-modular representations. We prove sharp lower bounds for this number in terms of p and the p′-part of the order of G which ensure that G is p-solvable. A bound for the p-length is obtained which is sharp for odd primes p. We also prove a new best possible criterion for the existence of a normal Sylow p-subgroup in terms of these quantities.

Modular binary octahedral symmetry for flavor structure of Standard Model

We have investigated the modular binary octahedral group 2O as a flavor symmetry to explain the structure of Standard Model. The vector-valued modular forms in all irreducible representations of this group are constructed. We have classified all possible fermion mass models based on the modular binary octahedral group 2O. A comprehensive numerical analysis is performed, and we present some benchmark quark/lepton mass models in good agreement with the experimental data. Notably we find a minimal modular invariant model for leptons and quarks, which is able to explain simultaneously the masses and mixing parameters of both quarks and leptons in terms of 14 real free parameters including the modulus τ. The fermion mass hierarchies around the vicinity of the modular fixed points are explored.

Determinants and Prevalence of Drug Abuse by Gender in the Selected Competitive Sports at the Universities in Kenya

Purpose: The main objective of this study was to identify the determinants and prevalence of drug abuse by gender in selected competitive sports at the universities in Kenya.
 Methodology: The study used a mixed methods research design with an intention to capture and utilise both qualitative and quantitative data. The study sample comprised 300 respondents. Out of the 300 students, 173 (57.7%) were male and 127 (42.3%) were female players derived from six selected competitive sports at the universities in Kenya. The selected sports were badminton, tennis, basketball, volleyball, soccer and rugby. Stratified sampling followed by simple random sampling was used to select 10 universities proportionately (4 private and 6 public), the method was the most appropriate to capture universities with women rugby in addition to the five other selected sports. The study sought to investigate the prevalence of drug abuse due to factors such as psychosocial, medicinal and competition. SPSS computer version 20 was used to process data. The data was presented in form of Tables.
 Findings: The study found that more male players than females abused drugs, with majority being rugby players. Findings indicated that there were more males than females abusing drugs at approximately 89% and 11% respectively. It was concluded that more male than female athletes engaging in sports in universities in Kenya, abuse drugs. This could be attributed to the assumption that males tend to experiment more on most things than do their female counterparts.
 Implications to Theory, Practice and Policy: The Social Learning Theory, SelfDetermination Theory and Harm Reduction Theory may be used to anchor future studies. It was recommended that various stakeholders that include the university management, NACADA and the security apparatus work together with an aim to sensitize and curb drug abuse menace among university athletes, general students’ community and the entire community bordering the universities

On the determinant of representations of generalized symmetric groups ℤ r ≀Sn

In this paper, we study the determinant of irreducible representations of the generalized symmetric groups Z r ≀ S n . We give an explicit formula to compute the determinant of an irreducible representation of Z r ≀ S n . Recently, several authors have characterized and counted the number of irreducible representations of a given finite group with nontrivial determinant. Motivated by these results, given an integer n, r an odd prime and ζ a nontrivial multiplicative character of Z r ≀ S n with n < r, we obtain an explicit formula to compute N ζ ( n ) , the number of irreducible representations of Z r ≀ S n whose determinant is ζ.

Analysis of a Multi-Server Queue with Group Service and Service Time Dependent on the Size of a Group as a Model of a Delivery System

In this paper, we consider a multi-server queue with a finite buffer. Request arrivals are defined by the Markov arrival process. Service is provided to groups of requests. The minimal and maximal group sizes are fixed. The service time of a group has a phase-type distribution with an irreducible representation depending on the size of the group. The requests are impatient. The patience time for an arbitrary request has an exponential distribution. After this time expires, the request is lost if all servers are busy or, if some server is idle, with a certain probability, all requests staying in the buffer start their service even if their number is below the required minimum. The behavior of the system is described by a multi-dimensional continuous-time Markov chain that does not belong to the class of level-independent quasi-birth-and-death processes. The algorithm for the computation of the stationary distribution of this chain is presented, and expressions for the computation of the queuing system’s performance characteristics are derived. The description of a delivery system operation in terms of the analyzed queuing model is given, and the problem of the optimization of its operation is numerically solved. Multi-server queues with a phase-type distribution for the group service time that are dependent on the size of the group, the account of request impatience, and the correlated arrival process have not previously been analyzed in the existing literature. However, they represent a precise model of many real-world objects, including delivery systems.

Enhancing pancreatic cancer classification through dynamic weighted ensemble: a game theory approach

The significant research carried out on medical healthcare networks is giving computing innovations lots of space to produce the most recent innovations. Pancreatic cancer, which ranks among of the most common tumors that are thought to be fatal and unsuspected since it is positioned in the region of the abdomen beyond the stomach and can’t be adequately treated once diagnosed. In radiological imaging, such as MRI and CT, computer-aided diagnosis (CAD), quantitative evaluations, and automated pancreatic cancer classification approaches are routinely provided. This study provides a dynamic weighted ensemble framework for pancreatic cancer classification inspired by game theory. Grey Level Co-occurrence Matrix (GLCM) is utilized for feature extraction, together with Gaussian kernel-based fuzzy rough sets theory (GKFRST) for feature reduction and the Random Forest (RF) classifier for categorization. The ResNet50 and VGG16 are used in the transfer learning (TL) paradigm. The combination of the outcomes from the TL paradigm and the RF classifier paradigm is suggested using an innovative ensemble classifier that relies on the game theory method. When compared with the current models, the ensemble technique considerably increases the pancreatic cancer classification accuracy and yields exceptional performance. The study improves the categorization of pancreatic cancer by using game theory, a mathematical paradigm that simulates strategic interactions. Because game theory has been not frequently used in the discipline of cancer categorization, this research is distinctive in its methodology.

Non-admissible irreducible representations of 𝑝-adic 𝐺𝐿_{𝑛} in characteristic 𝑝

Let p &gt; 3 p&gt;3 and F F be a non-archimedean local field with residue field a proper finite extension of F p \mathbb {F}_p . We construct smooth absolutely irreducible non-admissible representations of G L 2 ( F ) \mathrm {GL}_2(F) defined over the residue field of F F extending the earlier results of the authors for F F unramified over Q p \mathbb {Q}_{p} . This construction uses the theory of diagrams of Breuil and Pašk u ¯ \bar {\mathrm {u}} nas. By parabolic induction, we obtain smooth absolutely irreducible non-admissible representations of G L n ( F ) \mathrm {GL}_n(F) for n &gt; 2 n&gt;2 .