Classical solution of the Cauchy problem for biwave equation: Application of Fourier transform

In this paper, we use some Fourier analysis techniques to find an exact solution to the Cauchy problem for the $n$-dimensional biwave equation in the upper half-space $\mathbb{R}^n\times [0,+\infty)$.Comment: 11 page

単腕ロボットによる再利用性の高いひも結び動作の実現

電気通信大学201

Incidences between points and generalized spheres over finite fields and related problems

Let $\mathbb{F}_q$ be a finite field of $q$ elements where $q$ is a large odd prime power and $Q =a_1 x_1^{c_1}+...+a_dx_d^{c_d}\in \mathbb{F}_q[x_1,...,x_d]$, where $2\le c_i\le N$, $\gcd(c_i,q)=1$, and $a_i\in \mathbb{F}_q$ for all $1\le i\le d$. A $Q$-sphere is a set of the form $\lbrace x\in \mathbb{F}_q^d | Q(x-b)=r\rbrace$, where $b\in \mathbb{F}_q^d, r\in \mathbb{F}_q$. We prove bounds on the number of incidences between a point set $\mathcal{P}$ and a $Q$-sphere set $\mathcal{S}$, denoted by $I(\mathcal{P},\mathcal{S})$, as the following. $$| I(\mathcal{P},\mathcal{S})-\frac{|\mathcal{P}||\mathcal{S}|}{q}|\le q^{d/2}\sqrt{|\mathcal{P}||\mathcal{S}|}.$$ We prove this estimate by studying the spectra of directed graphs. We also give a version of this estimate over finite rings $\mathbb{Z}_q$ where $q$ is an odd integer. As a consequence of the above bounds, we give an estimate for the pinned distance problem. In Sections $4$ and $5$, we prove a bound on the number of incidences between a random point set and a random $Q$-sphere set in $\mathbb{F}_q^d$. We also study the finite field analogues of some combinatorial geometry problems, namely, the number of generalized isosceles triangles, and the existence of a large subset without repeated generalized distances.Comment: to appear in Forum Mat

Direct Strength Method for the Design of Cold-Formed Steel Sections Under Localised Loading

The main objective of the thesis is the development of the Direct Strength Method (DSM) for the design of cold-formed steel sections under general localised loading. In order to calibrate the DSM equations, it is necessary to have three main input variables which are the buckling load, the yield load and the experimental data. The first objective of this research is the development of the Finite Strip Method (FSM) theory for analysis of thin-walled sections under localised loading with general end boundary conditions to determine the buckling load as described in Chapters 3 and 4 of the thesis. The theory is included in Version 2.0 of the THIN-WALL-2 program which can be used for analysing structural members under generalised loading conditions as described in Chapter 5. The second objective is the formulation of plastic mechanism models to estimate the yield load of thin-walled sections subjected to localised loading. In order to establish these models, observations are performed from experiments to ascertain the failure modes of structural members under localised loading with different cross-sections, load cases and flange fastening conditions. From the data, new simple plastic mechanism models are built-up based on the concept of the balance between the internal energy of the structural member and the external energy of the applied loads to estimate the yield load as described in Chapter 6. The third objective is collating the experimental data of thin-walled sections under localised loading. The data is collected from previous literature for different types of cross-sections: un-lipped plain-C, lipped plain-C, SupaCee and Dimond Hi-Span channel (DHS) sections subjected to all load cases. In addition, both flange fastened and unfastened conditions are assembled in the experimental database as described in Chapter 6. From these three input variables, the DSM design equations are proposed for structural members under general localised loading. The method is a consistent and simplified model generalised for all localised load cases. It includes both an inelastic reserve component as observed in testing and a yield load component. Also, a reliability analysis calibration is performed to validate the accuracy of the DSM predictions with the collected experimental data as described in Chapter 7

Granular crystals in palm oil based shortening/margarine : a review

Palm oil based shortenings and margarines are important products within the lipid industry. However, a widespread quality deterioration issue is often reported regarding their long-term storage: the appearance of granular crystals or grains that are regarded as unwanted because of the deflecting visual appearance and the negative mouthfeel during consumption. In this review, the role of fat blends composition, crystallization process and storage conditions in the formation and growth of these unwanted granular crystals will be discussed and summarized. In addition, some potential approaches in preventing the formation of granular crystals in palm oil based shortening and margarine are also introduced

Factors that contribute to the pathogenesis of dengue in adult patients in Vietnam

Dengue fever and dengue hemorrhagic fever (DF /DHF) are caused by the dengue viruses, which belong to family Flaviviridae. DHF incidence has been increasing globally in the last 40 years. Over half the world's population lives in areas potentially at risk for dengue transmission, making dengue the most important human viral disease transmitted by arthropod vectors in terms of morbidity and mortality. Recently, the age distribution of DHF cases in Asia has changed. The number of adults with DHF has increased since the 1990s in Southeast Asian countries including Viet Nam. A series of studies were conducted in the Hospital for Tropical Diseases, Ho Chi Minh City, Viet Nam on clinical manifestations, cytokine production in acute infection and T cell responses in adult dengue patients