Abstract:
Let $G:=(V,E)$ be a simple graph; for $Isubseteq V$ we denote by $l(I)$ the number of components of $G[I]$, the subgraph of $G$ induced by $I$. For $V_1,ldots , V_n$ subsets of $V$, we define a function $eta (V_1,ldots , V_n)$ which is expressed in terms of $lleft(igcup _{i=1} ^{n} V_i ight)$ and $l(V_icup V_j)$ for $ileq j$. If $V_1,ldots , V_n$ are pairwise disjoint independent subsets of $V$, the number $eta (V_1,ldots , V_n)$ can be computed in terms of the cyclomatic numbers of $Gleft[igcup _{i=1} ^{n} V_i ight]$ and $G[ V_icup V_j]$ for $i eq j$. In the general case, we prove that $eta (V_1,ldots , V_n)geq 0$ and characterize when $eta (V_1,ldots , V_n)= 0$. This special case yields a formula expressing the length of members of an interval algebra cite{s} as well as extensions to pseudo-tree algebras. Other examples are given.

Abstract:
the authors report a case of isaacs syndrome observed in a 40 years old woman. the clinical picture included progressive muscular weakness, dysphagia, dysphonia, dyspnea and increased perspiration. fasciculations, facial myokymia and pseudomyotonia were observed on physical examination. electromyographic study at rest revealed continuous electrical muscle activity. muscle histochemistry showed type ii fibers atrophy and an ultrastructural study of the gastrocnemius muscle disclosed marked cysternal dilatation of the sarcoplasmatic reticulum. an excelent clinical response was observed with the use of carbamazepine. some recent aspects of this rare syndrome are reviewed and discussed.

Abstract:
FORMA DE ESTUDO: Clínico prospectivo. MATERIAL E MéTODO: Os autores avaliam a prevalência de altera es metabólicas em 325 pacientes que procuraram o Setor de Otoneurologia do Hospital das Clínicas da FMUSP com queixas vestibulares. Os pacientes foram consecutivamente atendidos entre janeiro de 1997 e janeiro de 2002. Foram avaliados os primeiros exames referentes ao protocolo clássico de investiga o das tonturas, que compreende a dosagem de LDL colesterol, TSH, T3 e T4 e glicemia de jejum. As altera es encontradas foram ent o comparadas às observadas na popula o geral. As altera es mais significativas encontradas foram a eleva o dos níveis de LDL colesterol, a presen a de níveis alterados de horm nios tireoideanos e a maior freqüência do diabetes mellitus na popula o estudada. CONCLUS O: Conclui-se que é válida a investiga o destes dados, visto que s o mais freqüentes na popula o de risco e que a correta abordagem dessas altera es melhora o prognóstico e o controle da tontura.

Abstract:
this paper deals with a certain way to investigate the mastering of technology by mathematics teachers and its use in their pedagogical practice. the instrumental approach which brings the suitable theoretical elements to this study is presented. this instrumental approach is supported by some psychological piaget's constructs, specially that one of schemata that is also assumed by vergnaud in his theory of conceptual fields. only the theoretical elements that make possible the understanding of a software implementation at mathematics lessons will be exposed. special attention is given to the concept of instrumental genesis in order to make the distinction between artifact and instrument, and between instrumentalization and instrumentation. results of an action-research realized with mathematics teachers are described based on those theoretical elements and on the proposed difference between inserting and integrating technology into the pedagogical practice in the mathematics teaching.

Abstract:
The aim of this study was to outline the seismologically active zones in Syria using the focal mechanisms of the largest events recorded by the Syrian National Seismological Network over the last decade. A dataset of fault-plane solutions was obtained for 49 events with magnitude ≥3.5 using the first P-wave motions. Most of these events had strike–slip mechanisms in agreement with the configuration of the seismogenic belts in Syria. Normal mechanisms were more scarce and were restricted to certain areas, such as the coastal ranges. These data show that despite the relatively small magnitudes of the events studied, they provide a coherent picture of the deformation that has currently been taking place along the active faults. However, some other faults were inactive during the period of this study.

Abstract:
study design: clinical prospective. material and method:the authors evaluated the prevalence of metabolic disorders among 325 patients with vestibular symptoms investigated by the otoneurology section, otolaryngology department of hospital das clínicas, medical school, university of s？o paulo. the patients were evaluated from january 1997 to january 2002, by a standard protocol which included, among other items, fast glucose levels, cholesterol, triglycerides and thyroid hormones, performed in the same laboratory. the results were compared to a standard population. results showed higher levels of fast glucose, alteration in the thyroid hormones and also higher prevalence of diabetes in the studied population. conclusion: the otolaryngologist should include the investigation of such medical problems in the routine evaluation in order to reverse them and to obtain better results in management of vestibular disorders.

Abstract:
The paper presents an approach for avoiding and minimizing the complementary pivots in a simplex based solution method for a quadratic programming problem. The linearization of the problem is slightly changed so that the simplex or interior point methods can solve with full speed. This is a big advantage as a complementary pivot algorithm will take roughly eight times as longer time to solve a quadratic program than the full speed simplex-method solving a linear problem of the same size. The strategy of the approach is in the assumption that the solution of the quadratic programming problem is near the feasible point closest to the stationary point assuming no constraints.

Abstract:
The energy size relationship is examined, either as the specific energy required breaking a particulate material from an initial size d_{1} to a final size d_{2}, where d is usually the d_{80} size, or as the specific energy required to break a single particle. The present work uses the results obtained using a controlled frequency centrifugal crusher to crush particles of a predetermined size class under different rotation frequencies related to the kinetic energy of the particles at the moment of crushing.The paper calculates the relationship between the rotation frequency and the kinetic energy of the particles before crushing and examines the size distribution of the products. The study results allow presenting the relationship between the kinetic energy of the particles and the mass of particles produced below the initial size class. The work also produces the optimum mathematical model that describes this relationship among three proposed ones. According to this model one can calculate the energy required breaking half of the initial mass below the initial size class and the corresponding specific energy is appointed to the average size of the class. The parameters of the mathematical model can be used to compare the grindability of the different materials. The process can be used as an alternative to the drop weight technique used so far for the study of the breakage energy of minerals and rocks.

The paper presents a technique for solving the binary linear programming model in polynomial time. The general binary linear programming problem is transformed into a convex quadratic programming problem. The convex quadratic programming problem is then solved by interior point algorithms. This settles one of the open problems of whether P = NP or not. The worst case complexity of interior point algorithms for the convex quadratic problem is polynomial. It can also be shown that every liner integer problem can be converted into binary linear problem.

Abstract:
age-related macular degeneration (armd) is a major source of legal blindness in individuals older than 50 years. even though recent reports suggest that genetics plays an important role, its pathogenesis remains puzzling and the risk factors for its occurrence are not completely established. vitamin and mineral supplementation reduced the risk of development of choroidal neovascularization (cnv) or progression to the most advanced stages of age-related macular degeneration. photodynamic therapy (pdt) and antiangiogenic therapy have proved to be very useful for the treatment of choroidal neovascularization associated to age-related macular degeneration, by reducing the risk of vision loss and, occasionally, by a temporary improvement of vision. only a small subset of patients may benefit from other treatment modalities, such as laser photocoagulation, surgical removal of choroidal neovascularization and transpuppillary thermotherapy (ttt). strategies to control and treat age-related macular degeneration may progress quickly as more is learned about its pathophysiology and the molecular events that contribute to the disease expression.