Optimization of Grouping Evacuation Strategy in High-rise Building Fires Based on Graph Theory and Computational Experiments

It is difficult to rescue people from outside, and emergency evacuation is still a main measure to decrease casualties in high-rise building fires. To improve evacuation efficiency, a valid and easily manipulated grouping evacuation strategy is proposed. Occupants escape in groups according to the shortest evacuation route is determined by graph theory. In order to evaluate and find the optimal grouping, computational experiments are performed to design and simulate the evacuation processes. A case study shown the application in detail and quantitative research conclusions is obtained. The thoughts and approaches of this study can be used to guide actual high-rise building evacuation processes in future.

Strategic group theory： A customer-oriented view

Barney and Hoskisson （1990） argue that the strategic group research has neither established the existence of strategic groups, nor their relationship to firm performance. The primary reason behind the unsatisfactory results is the lack of a theoretical framework： what strategic variables to include in the analysis and their relative importance; the definition of an industry, and how to make competitive strategy operational. First, the author presents a customer-oriented theory of management which submits that, like Procter and Gamble, understanding customers should be the primary focus of a business. Second, the author proposes an integrated approach to competitive strategy. Because customer-perceived quality is far more critical to long-term success than any other factor, it should be the centerpiece of competitive strategy. The author suggests that competitive strategy should be divided in two interdependent dimensions： external and internal. It is the external strategy that should be considered the primary dimension because it reflects the customers＇ perspective, and provides a sense of direction regarding how the internal resources should be used. Next, the author presents an operational framework of competitive strategy which proposes that the best route to market share leadership in consumer markets is competing in the mid-price segment, offering superior quality compared to competition at a somewhat higher price： （1） to maintain an image of quality, and （2） to ensure that the strategy is profitable and sustainable. Finally, the author offers a framework of business or industry definition that extends Abell＇s （1980） three dimensions to seven. He suggests that an integrated approach to market segmentation provides the foundation for conducting strategic group analysis in consumer markets. So, in strategic group research, we need a bottom-up approach that begins with a product-market segment. In each product market, real competition occurs at the brand level. This is the ground where actual competitive wars are fought, and this is where the rich dynamics of competition often come to light.

New Public Key Cryptosystems from Combinatorial Group Theory

External direct product of some low layer groups such as braid groups and general Artin groups, with a kind of special group action on it, provides a secure cryptographic computation platform, which can keep secure in the quantum computing epoch. Three hard problems on this new platform, Subgroup Root Problem, Multi-variant Subgroup Root Problem and Subgroup Action Problem are presented and well analyzed, which all have no relations with conjugacy. New secure public key encryption system and key agreement protocol are designed based on these hard problems. The new cryptosystems can be implemented in a general group environment other than in braid or Artin groups.

GROUP THEORY ANALYSIS OF MIXED CONVECTION OVER A HORIZONTAL MOVING PLATE

In the present paper, the investigation to the mixed convective boundary layer behavior over a horizontal plate is carried our. By applying transformation group theory, the analysis of the governing equations of continuity, momentum, energy and diffusion shows the existence of similarity solution for the problem provided that the temperature and concentration at the wall are proportional to x(4/(7-5n)) and that the moving speed of the plate is proportional to x((3-n)/(7-5n)), furthermore, a set of similarity equations is obtained. The similarity equations are solved numerically by a fourth-order Runge-Kutta scheme. The numerical results obtained for velocity, temperature and concentration distributions for Pr=0.72 and various values of the parameters Sc, K-1, K-2 and K-3 reveals the influence of these parameters on the flow, and hear and mass transfer behavior.

A New Group Theoretical Approach to the Nonorthogonal Problem in Valence Bond Theory

Introduction There has been a very significarnt resurgence of interest in ab initio valence bond calculations recently. This is because the VB calculation based on nonorthogonal basis can provide intuitive understanding about many very important phenomena in chemistry. However, practical calculation based on nonorthogonal basis is still a great challenge even to deal with a quite small system due to the well-known N! (or

Group of Weakly Continuous Operators Associated to a Generalized Schrödinger Type Homogeneous Model

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.

A symmetric substructuring method for analyzing the natural frequencies of conical origami structures

Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorptioncapacity.Previous investigations have commonly focused on the static characteristics of these lightweight struc-tures.However,the efficient analysis of the natural vibrations of these structures is pivotal for designing conicalorigami structures with programmable stiffness and mass.In this paper,we propose a novel method to analyzethe natural vibrations of such structures by combining a symmetric substructuring method(SSM)and a gener-alized eigenvalue analysis.SSM exploits the inherent symmetry of the structure to decompose it into a finiteset of repetitive substructures.In doing so,we reduce the dimensions of matrices and improve computationalefficiency by adopting the stiffness and mass matrices of the substructures in the generalized eigenvalue analysis.Finite element simulations of pin-jointed models are used to validate the computational results of the proposedapproach.Moreover,the parametric analysis of the structures demonstrates the influences of the number of seg-ments along the circumference and the radius of the cone on the structural mass and natural frequencies of thestructures.Furthermore,we present a comparison between six-fold and four-fold conical origami structures anddiscuss the influence of various geometric parameters on their natural frequencies.This study provides a strategyfor efficiently analyzing the natural vibration of symmetric origami structures and has the potential to contributeto the efficient design and customization of origami metastructures with programmable stiffness.

The Construction and Analysis of Linear Ring Spaces

This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The definition of quasi-linearity is discussed, in addition to the examination of properties and classifications of linear ring spaces. Particularly, the ring of holomorphic functions on a region of the complex plane is examined, and the manner in which it generates an iterated linear ring space under the complex derivative operator. This notion is then generalized to all rings with nth order linear and surjective operators. Basic operator theory regarding the classifications of linear ring maps is also covered.

Lie point symmetry algebras and finite transformation groups of the general Broer-Kaup system

Using a new symmetry group theory, the transformation groups and symmetries of the general Broer-Kaup system are obtained. The results are much simpler than those obtained via the standard approaches.

Group classification for path equation describing minimum drag work and symmetry reductions

The path equation describing the minimum drag work first proposed by Pakdemirli is reconsidered （Pakdemirli, M. The drag work minimization path for a fly- ing object with altitude-dependent drag parameters. Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science 223（5）, 1113- 1116 （2009））. The Lie group theory is applied to the general equation. The group classi- fication with respect to an altitude-dependent arbitrary function is presented. Using the symmetries, the group-invariant solutions are determined, and the reduction of order is performed by the canonical coordinates.

A Minimal Presentation of a Two-Generator Permutation Group on the Set of Integers

In this paper, we investigate the algebraic structure of certain 2-generator groups of permutations of the integers. The groups fall into two infinite classes: one class terminates with the quaternion group and the other class terminates with the Klein-four group. We show that all the groups are finitely presented and we determine minimal presentations in each case. Finally, we determine the order of each group.

A GROUP REPRESENTATION OF CANONICAL TRANSFORMATION

The mutual relationships between four generating functions F-1(q, Q), F-2(q, P), F-3(p, P), F-4(p, Q) and four kinds of canonical variables q, p, Q, P concerned in Hamilton's canonical transformations, can be got with linear transformations from seven basic formulae. All of them are Legendre's transformation, which are implemented by 32 matrices of 8 x 8 which are homomorphic to D-4 point group of 8 elements with correspondence of 4:1. Transformations and relationships of four state functions G(P, T), H(P, S), U(V, S), F(V, T) and four variables P, V, T, S in thermodynamics, are just the same Lagendre's transformations with the relationships of canonical transformations. The state functions of thermodynamics are summarily founded on experimental results of macroscope measurements, and Hamilton's canonical transformations are theoretical generalization of classical mechanics. Both group represents are the same, and it is to say, their mathematical frames are the same. This generality indicates the thermodynamical transformation is an example of one-dimensional Hamilton's canonical transformation.

Slope Stability Analysis Based on Group Decision Theory and Fuzzy Comprehensive Evaluation

A slope stability evaluation method is proposed combining group decision theory,the analytic hierarchy process and fuzzy comprehensive evaluation.The index weight assignment of each evaluation element is determined by group decision theory and the analytic hierarchy process,and the membership degree of each indicator is determined based on fuzzy set theory.According to the weights and memberships,the membership degrees of the criterion layer are obtained by fuzzy operations to evaluate the slope stability.The results show that(1)the evaluation method comprehensively combines the effects of multiple factors on the slope stability,and the evaluation results are accurate;(2)the evaluation method can fully leverage the experience of the expert group and effectively avoid evaluation errors caused by the subjective bias of a single expert;(3)based on a group decision theory entropy model,this evaluation method can quantitatively evaluate the reliability of expert decisions and effectively improve the efficiency of expert group discussion;and(4)the evaluation method can transform the originally fuzzy and subjective slope stability evaluation into a quantitative evaluation.

New Family of 3-DOF UP-Equivalent Parallel Mechanisms with High Rotational Capability

Parallel mechanisms(PMs) having the same motion characteristic with a UP kinematic chain(U denotes a universal joint, and P denotes a prismatic joint) are called UP-equivalent PMs. They can be used in many applications, such as machining and milling. However, the existing UP-equivalent PMs suffer from the disadvantages of strict assembly requirements and limited rotational capability. Type synthesis of UP-equivalent PMs with high rotational capability is presented.The special 2 R1 T motion is briefly discussed and the fact that the parallel module of the Exechon robot is not a UP-equivalent PM is disclosed. Using the Lie group theory, the kinematic bonds of limb chains and their mechanical generators are presented. Structural conditions for constructing such UP-equivalent PMs are proposed,which results in numerous new architectures of UP-equivalent PMs. The high rotational capability of the synthesized mechanisms is illustrated by an example. The advantages of no strict assembly requirements and high rotational capability of the newly developed PMs will facilitate their applications in the manufacturing industry.

Orientational Domains at Room Temperature in La_(0.33) Ca_(0.67) MnO_3 Perovskite

Orientational domains at room temperature in orthorhombic perovskite La 0.33 Ca 0.67 MnO 3 were studied by group theory and observed systematically using transmission electron microscopy. There are six orientational variants ( A, A', B,B', C and C' ) in orthorhombic perovskite La 0.33 Ca 0.67 MnO 3. Their orthorhombic b O directions are parallel to the a P, b P and c P directions of the cubic prototypic perovskite, respectively. In each case there are two orientational variants (e.g., A and A' ) with their a O and c O axes interchanged. Among the possible 15 boundaries between these 6 variants there are only two types of domain boundaries: (1) m<100> boundaries C'/C, A'/A, and B'/B. (2) m<110> boundaryies C'/A, C'/A', C'/B, C'/B', C/A, C/A', C/B, C/B', B'/A, B'/A', B/A, and B/A' .

Renormalization-group theory of first-order phase transition dynamics in field-driven scalar model

Through a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a φ^3 theory, we show that the instability fixed points of the theory, together with their associated instability exponents, are quite probably relevant to the scaling and universality behavior exhibited by the first-order phase transitions in a field-driven scalar Ca model, below its critical temperature and near the instability points. Finite- time scaling and leading corrections to the scaling are considered. We also show that the instability exponents of the first-order phase transitions are equivalent to those of the Yang-Lee edge singularity, and employ the latter to improve our estimates of the former. The outcomes agree well with existing numerical results.

Symmetries of boundary layer equations of power-law fluids of second grade

A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.

The U.S. Men＇s Shaving Cream Market： A Competitive Profile

Porter identifies high market share with cost leadership strategy which is based on the idea of competing on a price lower than that of the competition. However, in most consumer markets a business should serve the middle class by competing in the mid-price segment, offering quality better than that of the competition at a somewhat higher price. It is this path that can lead to market share leadership： a strategy that can be both profitable and sustainable. The U.S. men＇s shaving cream market consists of two major product-market segments： gel and foam. We test the hypothesis that the best-selling brand is very likely to be a member of the mid-price segment with a price tag that is higher than that of the nearest competition. This study is based on annual U.S. sales data for 2008 and 2007 from discount retail stores, food stores, and drug stores. We performed two separate analyses for 2008 and 2007, using cluster analysis as the main analytic tool. The results were remarkably consistent between the two years. In the gel segment--by far the most important--the price-quality segmentation analysis supported our hypothesis. An interesting finding is that, for both the gel and foam segments, we found the rank order correlation of brand unit price between 2007 and 2008 as highly significant. This means that in this market management considers the price of a brand as a strategic rather than a tactical variable. Although, technically the results for the foam segment were negative, this does not necessarily contradict our hypothesis. Finally, we discovered six strategic groups in the industry and have tried to articulate what their competitive strategy is.

Structural Synthesis of Parallel Mechanisms with High Rotational Capability

Most parallel mechanisms(PMs) encountered today have a common disadvantage, i.e., their low rotational capability.In order to develop PMs with high rotational capability, a family of novel manipulators with one or two dimensional rotations is proposed. The planar one-rotational one-translational(1 R1 T) and one-rotational two-translational(1 R2 T)PMs evolved from the crank-and-rocker mechanism(CRM) are presented by means of Lie group theory. A spatial 2 R1 T PM and a 2 R parallel moving platform with bifurcated large-angle rotations are proposed by orthogonal combination of the RRRR limbs. According to the product principle of the displacement group theory, a hybrid 2 R3 T mechanism in possession of bifurcated motion is obtained by connecting the 2 R parallel moving platform with a parallel part, which is constructed by four 3 T1 R kinematic chains. The presented manipulators possess high rotational capability. The proposed research enriches the family of spatial mechanisms and the construction method provides an instruction to design more complex mechanisms.

Plasmonics of regular shape particles,a simple group theory approach

A simple hand calculation method based on group theory is proposed to predict the near field maps of finite metallic nanoparticles(MNP)of canonical geometries:prism,cube,hexagon,disk,sphere,etc.corresponding to low order localized surface plasmon resonance excitations.In this article,we report the principles of the group theory approach and demonstrate,through several examples,the general character of the group theory method which can be applied to describe the plasmonic response of particles of finite or infinite symmetry point groups.Experimental validation is achieved by collection of high-resolution subwavelength near-field maps by photoemission electron microscopy(PEEM)on a representative set of Au colloidal particles exhibiting either finite(hexagon)or infinite(disk,sphere)symmetry point groups.