Observability of string vibrations

Transversal vibrations $u=u(x,t)$ of a string of length $l$ under three essential boundary conditions are studied, where $u$ is governed by the Klein--Gordon equation: $$u_{tt}(x,t) = a^2u_{xx}(x,t) - cu(x,t), (x,t) \in [0,l]\times \mathbb{R}; \ 0 < a, c \in \mathbb{R}.$$ Sufficient conditions are obtained that guarantee the unique solvability of a general observation problem with the given state functions $f, g \in D^s(0,l), s \in \mathbb{R}$ at two distinct instants of time $-\infty < t_1 < t_2 < \infty$: \begin{array} \displaystyle A_1 u|_{t=t_1} + B_1 u_t|_{t=t_1} = f, & |A_1|+|B_1| > 0, \ A_1 B_1\geq 0, \\ \displaystyle A_2 u|_{t=t_2} + B_2 u_t|_{t=t_2} = g, & |A_2|+|B_2| > 0, \ A_2 B_2\leq 0. \end{array} Here $s$ is arbitrary, the space $D^s(0,l)$ (see [2] and [13]) is some subspace of the Sobolev space $H^s(0,l)$. The essential condition of the solvability is that $(t_2-t_1) a/l$ is a rational number. In fact, this result is a consequence of a general observability result related to the vibration $u = u(x,t)$ governed by the equation $$u_{tt} = (p(x) u_{x})_x - q(x) u, (x,t)\in [0,l]\times \mathbb{R}, 0 < p, q \in C^{\infty}([0,l]),$$ subject to some initial data and linear boundary conditions (see in Proposition 1 below). This time the main restrictions are some Diophantine conditions and asymptotic properties of the eigenfrequencies $\omega_n$ as $n \to \infty$. Some other results without these restrictions are also presented

Observation problems posed for the Klein-Gordon equation

Transversal vibrations $u=u(x,t)$ of a string of length $l$ with fixed ends are considered, where $u$ is governed by the Klein-Gordon equation $$u_{tt}(x,t) = a^2u_{xx}(x,t)+cu(x,t), \qquad (x,t) \in [0,l] \times \mathbb{R}, \quad a>0, \ c<0.$$ Sufficient conditions are obtained that guarantee the solvability of each of four observation problems with given state functions $f, \ g$ at two distinct time instants $-\infty<t_1<t_2 < \infty$. The essential conditions are the following: smoothness of $f, \ g$ as elements of a corresponding subspace $D^{s+i}(0,l)$ (introduced in [2]) of a Sobolev space $H^{s+i} (0,l)$, where $i=1,2$ depending on the type of the observation problem, and the representability of $t_2-t_1$ as a rational multiple of $\frac{2l}{a}$. The reconstruction of the unknown initial data $(u(x,0), u_t(x,0))$ as the elements of $D^{s+1}(0,l) \times D^s(0,l)$ are given by means of the method of Fourier expansions

Five loop Konishi from AdS/CFT

We derive the perturbative five loop anomalous dimension of the Konishi operator in N = 4 SYM theory from the integrable string sigma model by evaluating finite size effects using Luscher formulas adapted to multimagnon states at weak coupling. In addition, we derive the five loop wrapping contribution for the L = 2 single impurity state in the beta deformed theory, which may be within reach of a direct perturbative computation. The Konishi expression exhibits two new features - a modification of Asymptotic Bethe Ansatz quantization and sensitiveness to an infinite set of coefficients of the BES/BHL dressing phase. The result satisfies nontrivial self-consistency conditions - simple transcendentality structure and cancellation of mu-term poles. It may be a testing ground for the proposed AdS/CIFT TBA systems. (C) 2009 Elsevier B.V. All rights reserved

A Comparison of the Genetic Shaft Types of Some Karst Areas Based on Their Specific Shaft Lengths

Shaft development can be documented on the basis of comparative studiesof specific shaft lengths and shaft patterns. We calculated the specific lengthof shafts and the average specific shaft length of the shafts in some karstareas and we investigated the relation between the altitude of shaft floorsand the specific shaft length. Taking the registered specific shaft lengthsand the shaft patterns into consideration, it can be stated that some partsof the shafts developed paragenetically in the studied karst areas. In theBakony Region, this was caused by surface water influx, rise of karst waterlevel, and their simultaneous effect. As a result, shaft systems, bifurcatingshafts and storeyed shafts developed. On glaciokarst areas, shafts mayconstitute a system with phreatic passages: either because a phreatic environment developed in the vadose zone due to the permanent impoundmentof karst water or because a phreatic passage got into the vadose zone sincethe karst became elevated. On the studied karst areas, the following shaftdevelopment types are distinguished: glacial-high mountain surface flooddevelopment type (1), glacial-high mountain karst water and surface flooddevelopment type (2), glacial karst water and surface flood later phreaticdevelopment type (3), shaft with a passage that got into the vadose zone (4)

Preliminary characterization of the self-incompatibility genotypes of European plum (Prunus domestica L.) cultivars

European plum is an important fruit crop with complex, hexaploid genome of unknown origin. The characterization of the selfincompatibility(S) locus of 16 European plum cultivars was carried out using the PaConsI-F primer in combination with the EM-PC1consRDprimer for the first intron and the EM-PC2consFD and EM-PC3consRD primers for the second intron amplification. Altogether, 18 differentalleles were scored indicating high genetic diversity. These alleles were labelled using alphabetical codes from SA to SS. We identified 5different alleles in 9 cultivars, 4 alleles in 5 cultivars, while 3 alleles were shown in two of the assayed cultivars. A total of 16 differentS-genotypes were assigned, and discrimination of all plum cultivars was successful based on their unique S-genotypes. However, furtherresearch is required to reliably identify the S-alleles based on their DNA sequence and clarify complete S-genotypes

Preliminary characterization of the self-incompatibility genotypes of European plum (Prunus domestica L.) cultivars

European plum is an important fruit crop with complex, hexaploid genome of unknown origin. The characterization of the selfincompatibility (S) locus of 16 European plum cultivars was carried out using the PaConsI-F primer in combination with the EM-PC1consRD primer for the first intron and the EM-PC2consFD and EM-PC3consRD primers for the second intron amplification. Altogether, 18 different alleles were scored indicating high genetic diversity. These alleles were labelled using alphabetical codes from SA to SS. We&nbsp; identified 5 different alleles in 9 cultivars, 4 alleles in 5 cultivars, while 3 alleles were shown in two of the assayed cultivars. A total of 16 different S-genotypes were assigned, and discrimination of all plum cultivars was successful based on their unique S-genotypes. However, further research is required to reliably identify the S-alleles based on their DNA sequence and clarify complete S-genotypes

review of nutritional value and putative health-effects of quince (Cydonia oblonga Mill.) fruit

Quince (Cydonia oblonga Mill.) has been long regarded to be a health-promoting fruit. Although it is mainlyconsumed in processed form, its relatively heat-stable polyphenolics were confi rmed to be responsible for most of the benefi cialeffects. This review aims to show basic nutritional information on quince fruit such as carbohydrate, fi bre, pectin and mineralelement contents. In addition, vitamin and polyphenolic contents and composition as well as the physiological effects of quinceconsumption were also surveyed. Information on presumable protective effects against several diseases including infl ammation,atopic dermatitis, ulcers and cancer is summarized. Potential antibacterial effects of quince polyphenolics were also considered.Polyphenolics are supposed to be responsible for the major part of benefi cial health-effects, and phenolic compoundspredominantly accumulate in peel. There exists a considerable extent of genetic variation in phytochemical composition amongcultivars, which might be exploited in designing future breeding programs for quince improvement and opening new ways forhealth-related uses