Nontrivial Factor Research Articles

De Sitter space in gauge/gravity duality

We investigate gauge/gravity duality for gauge theories in de Sitter space. More precisely, we study a five-dimensional consistent truncation of type IIB supergravity, which encompasses a wide variety of gravity duals of strongly coupled gauge theories, including the Maldacena–Nunez solution and its walking deformations. We find several solutions of the 5d theory with dS4 spacetime and nontrivial profiles for (some of) the scalars along the fifth (radial) direction. In the process, we prove that one of the equations of motion becomes dependent on the others, for nontrivial warp factor. This dependence reduces the number of field equations and, thus, turns out to be crucial for the existence of solutions with (A)dS4 spacetime. Finally, we comment on the implications of our dS4 solutions for building gravity duals of Glueball Inflation.

Mixing actions of countable groups are almost free

A measure preserving action of a countably infinite group \Gamma is called totally ergodic if every infinite subgroup of \Gamma acts ergodically. For example, all mixing and mildly mixing actions are totally ergodic. This note shows that if an action of \Gamma is totally ergodic then there exists a finite normal subgroup N of \Gamma such that the stabilizer of almost every point is equal to N. Surprisingly the proof relies on the group theoretic fact (proved by Hall and Kulatilaka as well as by Kargapolov) that every infinite locally finite group contains an infinite abelian subgroup, of which all known proofs rely on the Feit-Thompson theorem. As a consequence we deduce a group theoretic characterization of countable groups whose non-trivial Bernoulli factors are all free: these are precisely the groups that posses no finite normal subgroup other than the trivial subgroup.

AVERAGE WEIGHTED RECEIVING TIME OF WEIGHTED TETRAHEDRON KOCH NETWORKS

We introduce weighted tetrahedron Koch networks with infinite weight factors, which are generalization of finite ones. The term of weighted time is firstly defined in this literature. The mean weighted first-passing time (MWFPT) and the average weighted receiving time (AWRT) are defined by weighted time accordingly. We study the AWRT with weight-dependent walk. Results show that the AWRT for a nontrivial weight factor sequence grows sublinearly with the network order. To investigate the reason of sublinearity, the average receiving time (ART) for four cases are discussed.

Factorization and Criticality in the Anisotropic XY Chain via Correlations

In this review, we discuss the zero and finite temperature behavior of various bipartite quantum and total correlation measures, the skew information-based quantum coherence and the local quantum uncertainty in the thermal ground state of the one-dimensional anisotropic XY model in a transverse magnetic field. We compare the ability of the considered measures to correctly detect or estimate the quantum critical point and the non-trivial factorization point possessed by the spin chain.

Quantum phase transition as an interplay of Kitaev and Ising interactions

We study the interplay between the Kitaev and Ising interactions on both ladder and two dimensional lattices. We show that the ground state of the Kitaev ladder is a symmetry-protected topological (SPT) phase, which is protected by a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry. It is confirmed by the degeneracy of the entanglement spectrum and non-trivial phase factors (inequivalent projective representations of the symmetries), which are obtained within infinite matrix-product representation of numerical density matrix renormalization group. We derive the effective theory to describe the topological phase transition on both ladder and two-dimensional lattices, which is given by the transverse field Ising model with/without next-nearest neighbor coupling. The ladder has three phases, namely, the Kitaev SPT, symmetry broken ferro/antiferromagnetic order and classical spin-liquid. The non-zero quantum critical point and its corresponding central charge are provided by the effective theory, which are in full agreement with the numerical results, i.e., the divergence of entanglement entropy at the critical point, change of the entanglement spectrum degeneracy and a drop in the ground-state fidelity. The central charge of the critical points are either c=1 or c=2, with the magnetization and correlation exponents being 1/4 and 1/2, respectively. In the absence of frustration, the 2D lattice shows a topological phase transition from the $\mathbb{Z}_2$ spin-liquid state to the long-range ordered Ising phase at finite ratio of couplings, while in the presence of frustration, an order-by-disorder transition is induced by the Kitaev term. The 2D classical spin-liquid phase is unstable against the addition of Kitaev term toward an ordered phase before the transition to the $\mathbb{Z}_2$ spin-liquid state.

Simple mixing actions with uncountably many prime factors

Via the $(C,F)$-construction we produce a 2-fold simple mixing transformation which has uncountably many non-trivial proper factors and all of them are prime.

Squarefree values of trinomial discriminants

AbstractThe discriminant of a trinomial of the form $x^{n}\pm \,x^{m}\pm \,1$ has the form $\pm n^{n}\pm (n-m)^{n-m}m^{m}$ if $n$ and $m$ are relatively prime. We investigate when these discriminants have nontrivial square factors. We explain various unlikely-seeming parametric families of square factors of these discriminant values: for example, when $n$ is congruent to 2 (mod 6) we have that $((n^{2}-n+1)/3)^{2}$ always divides $n^{n}-(n-1)^{n-1}$. In addition, we discover many other square factors of these discriminants that do not fit into these parametric families. The set of primes whose squares can divide these sporadic values as $n$ varies seems to be independent of $m$, and this set can be seen as a generalization of the Wieferich primes, those primes $p$ such that $2^{p}$ is congruent to 2 (mod $p^{2}$). We provide heuristics for the density of these sporadic primes and the density of squarefree values of these trinomial discriminants.

On the partitions with Sturmian-like refinements

In the dynamics of a rotation of the unit circle by an irrational angle $\alpha\in(0,1)$, we study the evolution of partitions whose atoms are finite unions of left-closed right-open intervals with endpoints lying on the past trajectory of the point $0$.Unlike the standard framework, we focus on partitions whose atoms are disconnected sets.We show that the refinements of these partitions eventually coincide with the refinements of a preimage of the Sturmian partition, which consists of two intervals $[0,1-\alpha)$ and $[1-\alpha,1)$.In particular, the refinements of the partitions eventually consist of connected sets, i.e., intervals. We reformulate this result in terms of Sturmian subshifts: we show that for every non-trivial factor mapping from a one-sided Sturmian subshift, satisfying a mild technical assumption, the sliding block code of sufficiently large length induced by the mapping is injective.

Sizable electron/neutron electric dipole moment inD3/D7μ-split supersymmetry

Within the framework of $\mathcal{N}=1$ gauged supergravity, using a phenomenological model that can be obtained locally as a Swiss-cheese Calabi-Yau string-theoretic compactification with a mobile $D3$-brane localized on a nearly special Lagrangian three cycle in the Calabi-Yau and fluxed stacks of wrapped $D7$-branes, and which provides a natural realization of $\ensuremath{\mu}$-split supersymmetry (SUSY), we show that in addition to getting a significant value of an [electron/neutron (e/n)] electron dipole moment (EDM) at two-loop level, one can obtain a sizable contribution of (e/n) EDM even at one-loop level due to the presence of heavy supersymmetric fermions nearly isospectral with heavy sfermions. Unlike traditional split SUSY models in which the one-loop diagrams do not give significant contribution to the EDM of the electron/neutron because of very heavy sfermions existing as propagators in the loop, we show that one obtains a ``healthy'' value of the EDM in our model because of the presence of a heavy Higgsino, neutralino/chargino, and gaugino as fermionic propagators in the loops. The independent $CP$-violating phases are generated from nontrivial distinct phase factors associated with four Wilson line moduli [identified with first-generation leptons and quarks and their $SU(2{)}_{L}$-singlet cousins] as well as the $D3$-brane position moduli (identified with two Higgses), and the same are sufficient to produce overall distinct phase factors corresponding to all possible effective Yukawas as well as effective gauge couplings that we discuss in the context of $\mathcal{N}=1$ gauged supergravity action. However, the complex phases responsible to generate a nonzero EDM at one-loop level mainly appear from an off-diagonal contribution of sfermion as well as Higgs mass matrices at the electroweak scale (EW). In our analysis, we obtain a dominant contribution of the electron/neutron EDM around ${d}_{e}/e\ensuremath{\equiv}\mathcal{O}(1{0}^{\ensuremath{-}29})\text{ }\text{ }\mathrm{cm}$ from two-loop diagrams involving heavy sfermions and a light Higgs, and ${d}_{e}/e\ensuremath{\equiv}\mathcal{O}(1{0}^{\ensuremath{-}32})\text{ }\text{ }\mathrm{cm}$ from a one-loop diagram involving a heavy chargino and a light Higgs as propagators in the loop. The neutron EDM gets a dominant contribution of the order ${d}_{n}/e\ensuremath{\equiv}\mathcal{O}(1{0}^{\ensuremath{-}33})\text{ }\text{ }\mathrm{cm}$ from the one-loop diagram involving SM-like quarks and Higgs. To justify the possibility of obtaining a large EDM value in the case of a Barr-Zee diagram which involves ${W}^{\ifmmode\pm\else\textpm\fi{}}$ and the Higgs (responsible to generate the nontrivial $CP$-violating phase) in the two-loop diagrams as discussed by Leigh et al. [Nucl. Phys. B267, 509 (1986)], we provide an analysis of the same in the context of our $D3/D7$ $\ensuremath{\mu}$-split SUSY model at the EW scale. By conjecturing that the $CP$-violating phase can appear from the diagonalization of the Higgs mass matrix obtained in the context of $\ensuremath{\mu}$-split SUSY, we also get an EDM of the electron/neutron around $\mathcal{O}(1{0}^{\ensuremath{-}27})\text{ }\text{ }e\text{ }\mathrm{cm}$ in the case of the two-loop diagram involving ${W}^{\ifmmode\pm\else\textpm\fi{}}$ bosons.

Natural factors of the Medvedev lattice capturing IPC

Skvortsova showed that there is a factor of the Medvedev lattice which captures intuitionistic propositional logic (IPC). However, her factor is unnatural in the sense that it is constructed in an ad hoc manner. We present a more natural example of such a factor. We also show that the theory of every non-trivial factor of the Medvedev lattice is contained in Jankov’s logic, the deductive closure of IPC plus the weak law of the excluded middle $${\neg p \vee \neg \neg p}$$ . This answers a question by Sorbi and Terwijn.

Bernoulli actions of sofic groups have completely positive entropy

We prove that every Bernoulli action of a sofic group has completely positive entropy with respect to every sofic approximation net. We also prove that every Bernoulli action of a finitely generated free group has the property that each of its nontrivial factors with a finite generating partition has positive f-invariant.

Getting real about BIM

Purpose – For some years, it has been claimed that Building Information Modelling (BIM) will bring about major improvements to the productivity of the building industry. Yet, productivity has declined while claims for BIM have expanded. Often, BIM descriptions comprise the naïve framing and multiple fallacies of hype. The purpose of this paper is to present critical realist descriptions and explain their advantages compared to BIM hype descriptions. Design/methodology/approach – A longitudinal critical realist case study of BIM causal mechanism and causal context. Findings – Critical realist analysis reveals that hype about BIM underplays many inter-related causal requirements: all of which are needed to bring project business outcome from management action. Practical implications – Many inter-related non-trivial causal factors need to be taken into account to achieve business outcome from BIM implementation action. Further, factors claimed at the outset to be adequate to achieve outcome from action may be less than adequate. Originality/value – The originality of this paper is that critical realism analysis across six years is presented. This longitudinal data reveals that claims for BIM can be more future goals than current certainties. The value of this paper is that detailed analysis of hype descriptions is provided alongside critical realist descriptions.

Nodal domains of the equilateral triangle billiard

We characterize the eigenfunctions of an equilateral triangle billiard in terms of its nodal domains. The number of nodal domains has a quadratic form in terms of the quantum numbers, with a non-trivial number-theoretic factor. The patterns of the eigenfunctions follow a group-theoretic connection in a way that makes them predictable as one goes from one state to another. Extensive numerical investigations bring out the distribution functions of the mode number and signed areas. The statistics of the boundary intersections is also treated analytically. Finally, the distribution functions of the nodal loop count and the nodal counting function are shown to contain information about the classical periodic orbits using the semiclassical trace formula. We believe that the results belong generically to non-separable systems, thus extending the previous works which are concentrated on separable and chaotic systems.

Data Retrieval Scheduling for Multi-Item Requests in Multi-Channel Wireless Broadcast Environments

Wireless data broadcast is a popular data dissemination method in mobile computing environments because of its capability of concurrently disseminating data to multiple users. In this paper, we study the data retrieval scheduling problem for multi-item requests in multi-channel broadcast environments. To maximize the number of downloads given a deadline, we define a problem called largest number data retrieval (LNDR). We prove the decision problem of LNDR is NP-hard, and we investigate approximation algorithm for it. We also define another problem called minimum cost data retrieval (MCDR), which aims at downloading a set of requested data items with the least response time and energy consumption. We prove MCDR is NP-hard to approximate to within any non-trivial factor. Therefore, we investigate heuristic algorithm for it. Finally we provide simulation results to demonstrate the practical efficiency of the proposed algorithms.

The Hopfian property of n-periodic products of groups

Let $H$ be a subgroup of a group $G$. A normal subgroup $N_H$ of $H$ is said to be inheritably normal if there is a normal subgroup $N_G$ of $G$ such that $N_H=N_G\cap H$. It is proved in the paper that a subgroup $N_{G_i}$ of a factor $G_i$ of the $n$-periodic product $\prod_{i\in I}^nG_i$ with nontrivial factors $G_i$ is an inheritably normal subgroup if and only if $N_{G_i}$ contains the subgroup $G_i^n$. It is also proved that for odd $n\ge 665$ every nontrivial normal subgroup in a given $n$-periodic product $G=\prod_{i\in I}^nG_i$ contains the subgroup $G^n$. It follows that almost all $n$-periodic products $G=G_1\overset{n}{\ast}G_2$ are Hopfian, i.e., they are not isomorphic to any of their proper quotient groups. This allows one to construct nonsimple and not residually finite Hopfian groups of bounded exponents.

Quantized Abelian Principal Connections on Lorentzian Manifolds

We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work within an appropriate differential geometric setting by using the bundle of connections and we study the full gauge group, namely the group of vertical principal bundle automorphisms. Properties of our functor are investigated in detail and, similar to earlier works, it is found that due to topological obstructions the locality property of locally covariant quantum field theory is violated. Furthermore, we prove that, for Abelian structure groups containing a nontrivial compact factor, the gauge invariant Borchers-Uhlmann algebra of the vector dual of the bundle of connections is not separating on gauge equivalence classes of principal connections. We introduce a topological generalization of the concept of locally covariant quantum fields. As examples, we construct for the category of principal U(1)-bundles two natural transformations from singular homology functors to the quantum field theory functor that can be interpreted as the Chern class and the electric charge. In this case we also prove that the electric charges can be consistently set to zero, which yields another quantum field theory functor that satisfies all axioms of locally covariant quantum field theory.

Effect of environmental variables on Green Buying Intention in different Purchase Situations

Green Marketing acquired high importance due to governmental regulations applicable across sectors. These regulations follow global changes in economic relations, political alignments, environmental treaties and technological developments. As per Raju et al (2012), biofuel production in India increased from 0.01 million tonnes to 21.0 million tonnes in 2010. Different climate change conferences like the one concluded in Doha recently influence global view on sustainability. Industry also follows the global view and has embraced Green Marketing. Many firms have upgraded to environment friendly technology and have modified their promotions. This includes new greener products by Unilever, ITC, McDonalds, Whirlpool, Indian Oil, Wipro, and Nerolac. This also includes environment friendly services by Tata group, State Bank of India and others in India. Consumer research on analyzing effect of such factors on consumer purchase intention in different buying situations is yet to be done. This research aims to study effect of these environmental variables on Green Buying Intention in different Purchase Situations. Participants had to choose one out of six listed products that they can recall to have bought recently. Questions utilized Likert-type scale for six preference options. Elements of Marketing Mix varied were product quality (product), price, promotion and availability (place). Determination of factors is done by utilizing procedures (Bryant and Yarnold, 1995; Brown, 2009; Malhotra and Dash, 2009) of Percent of Cumulative Variance, Kaiser’s Stopping Rule, Scree Test, Number of non-trivial factors and Split-half reliability. Consumers’ preference towards green products is higher if these provide combination of societal benefit, environmental benefit, economic sense and improved technology. Example of this is usage of CNG driven vehicles in cities like Delhi, India. This required consumer to first incur expenses and then recover those by reduced cost of usage. In case of Extended PSBS, GovtRegulation has ‘very good’ factor loading on first component. Consumers have relatively high abundance of time and there is high involvement of consumer in case of Extended PSBS like buying of a car/house. Implications: Efforts in Green Marketing need to be differently focused in different buying conditions. On one hand, some factors affect both types of purchase situations. Companies need to ensure that Society, Environment, Economy, and Technology should be given due importance in their overall green marketing programs irrespective of the type of purchase situation. On the other hand, Quality and Govt Regulation behave differently in each purchase situation. In good economic conditions, a product of habitual PSBS having good quality and availability will be bought by consumers readily. Also, consumers in habitual PSBS intend to purchase a green product if regulation supports promotion and price. Contrast this with Extended PSBS, in which Quality combines with Technology and Price since consumers take long time in deciding the final alternative in this buying situation. Also, Govt Regulation combines with other macro factors like Society, Environment and Economy to indicate that sustainable products in case of Extended PSBS need acceptance by Society and Economy along with regulations by the Government. Therefore, Purchase situation plays key role in shaping purchase intention of consumers. Companies have to consider the type of purchase situation in designing their Green Marketing programs.

Deterministic polynomial factoring and association schemes

AbstractThe problem of finding a nontrivial factor of a polynomial$f(x)$over a finite field${\mathbb{F}}_q$has many known efficient, but randomized, algorithms. The deterministic complexity of this problem is a famous open question even assuming the generalized Riemann hypothesis (GRH). In this work we improve the state of the art by focusing on prime degree polynomials; let$n$be the degree. If$(n-1)$has a ‘large’$r$-smooth divisor$s$, then we find a nontrivial factor of$f(x)$in deterministic$\mbox{poly}(n^r,\log q)$time, assuming GRH and that$s=\Omega (\sqrt{n/2^r})$. Thus, for$r=O(1)$our algorithm is polynomial time. Further, for$r=\Omega (\log \log n)$there are infinitely many prime degrees$n$for which our algorithm is applicable and better than the best known, assuming GRH. Our methods build on the algebraic-combinatorial framework of$m$-schemes initiated by Ivanyos, Karpinski and Saxena (ISSAC 2009). We show that the$m$-scheme on$n$points, implicitly appearing in our factoring algorithm, has an exceptional structure, leading us to the improved time complexity. Our structure theorem proves the existence of small intersection numbers in any association scheme that has many relations, and roughly equal valencies and indistinguishing numbers.

A unified approach to model uptake kinetics of trace elements in complex aqueous – solid solution systems

Thermodynamics alone is usually not sufficient to predict growth-rate dependencies of trace element partitioning into host mineral solid solutions. In this contribution, two uptake kinetic models were analyzed that are promising in terms of mechanistic understanding and potential for implementation in geochemical modelling codes. The growth Surface Entrapment Model (Watson, 2004) and the Surface Reaction Kinetic Model (DePaolo, 2011) were shown to be complementary, and under certain assumptions merged into a single analytical expression. This Unified Uptake Kinetics Model was implemented in GEMS3K and GEM-Selektor codes (http://gems.web.psi.ch), a Gibbs energy minimization package for geochemical modelling. This implementation extends the applicability of the unified uptake kinetics model to accounting for non-trivial factors influencing the trace element partitioning into solid solutions, such as the changes in aqueous solution composition and speciation, or the depletion effects in closed geochemical systems.

Supersymmetric gauge theories on a squashed four-sphere

We define a squashed four-sphere by a dimensional reduction of a twisted S 4 × S 1, and construct explicitly a supersymmetric Yang-Mills action on it. The action includes a non-trivial dilaton factor and a theta term with a non-constant theta. The partition function of this theory is calculated using the localization technique. The resulting partition function can be written in the form consistent with the AGT relation due to the non-constant theta term. The parameter b which characterizes the partition function in this form is not restricted to be real for the squashed four-sphere.