On the Distribution of the Number of Points on Algebraic Curves in Extensions of Finite Fields

Let \cC be a smooth absolutely irreducible curve of genus $g \ge 1$ defined over \F_q, the finite field of $q$ elements. Let # \cC(\F_{q^n}) be the number of \F_{q^n}-rational points on \cC. Under a certain multiplicative independence condition on the roots of the zeta-function of \cC, we derive an asymptotic formula for the number of $n =1, ..., N$ such that (# \cC(\F_{q^n}) - q^n -1)/2gq^{n/2} belongs to a given interval \cI \subseteq [-1,1]. This can be considered as an analogue of the Sato-Tate distribution which covers the case when the curve \E is defined over \Q and considered modulo consecutive primes $p$, although in our scenario the distribution function is different. The above multiplicative independence condition has, recently, been considered by E. Kowalski in statistical settings. It is trivially satisfied for ordinary elliptic curves and we also establish it for a natural family of curves of genus $g=2$.Comment: 14 page

Multiplicative Order of Gauss Periods

We obtain a lower bound on the multiplicative order of Gauss periods which generate normal bases over finite fields. This bound improves the previous bound of J. von zur Gathen and I. E. Shparlinski.Comment: 9 page

Identifying Contextual Predictors Of Urban Park Utilization Among Inter-Ethnic Groups In Malaysia

Social interaction among diverse ethnic groups motivates people within communities to visit urban parks towards achieving social cohesion. Malaysians of different ethnic backgrounds spend their leisure time in urban parks because it offers opportunities for social interaction. The perception and requirement of attributes needed varies among the various ethnic groups of Malays, Chinese and Indians in order to be assured of their full utilization of the parks. This study investigates the urban park attributes that encourage the utilization of urban park by these three ethnic groups toward achieving social cohesion. Using a survey questionnaire method a total of 274 respondents were sampled at Batu Pahat urban parks in Johor, Malaysia. Afterwards, Structural Equation Modelling (SEM) was used to analyse and validate respondents’ perception of urban park utilization. The findings show that aesthetics, safety, lighting, maintenance and cleanliness in public spaces attracted people to visit the urban park and contributed towards social cohesion

ON STABLE QUADRATIC POLYNOMIALS

We recall that a polynomial f(X) ∈ K[X] over a field K is called stable if all its iterates are irreducible over K. We show that almost all monic quadratic polynomials f(X) ∈ ℤ[X] are stable over ℚ. We also show that the presence of squares in so-called critical orbits of a quadratic polynomial f(X) ∈ ℤ[X] can be detected by a finite algorithm; this property is closely related to the stability of f(X). We also prove there are no stable quadratic polynomials over finite fields of characteristic 2 but they exist over some infinite fields of characteristic

Hemodialysis, plea of availability versus adequecy gezira experience

Objectives: This is a prospective cross sectional study carried out in Gezira Hospital for Renal Diseases and Surgery (Sudan) to assess the adequacy of hemodialysis in 206 patients with end stage kidney disease on regular hemodialysis twice per week using.Methods: Pre and post hemodialysis blood sample were obtained from the study group, spKt/V and urea reduction ratio were calculated.Results: Mean Kt/v was found to be 1.19 and urea reduction ratio was 59.55%. None of the patients in this study group achieved the National Kidney Foundation Dialysis Outcomes Quality Initiative (K/DOQI) recommendations for adequate hemodialyis, since it requiresthree hemodialyis sessions per week and our patients are receiving two sessions per week.Conclusion: In order to improve the situation herewith we recommended increased number of sessions from two to three times per week and \or increase the duration of hemodialysis session, increase blood flow rate and dialysate flow rate. Moreover, decrease the number of patients onregular hemodialysis by encouraging the patients to take the other renal replacement therapy (peritoneal dialysis and renal transplantations)

Hyperinsulinism-hyperammonaemia syndrome: novel mutations in the GLUD1 gene and genotype-phenotype correlations

Background: Activating mutations in the GLUD1 gene (which encodes for the intra-mitochondrial enzyme glutamate dehydrogenase, GDH) cause the hyperinsulinism–hyperammonaemia (HI/HA) syndrome. Patients present with HA and leucine-sensitive hypoglycaemia. GDH is regulated by another intra-mitochondrial enzyme sirtuin 4 (SIRT4). Sirt4 knockout mice demonstrate activation of GDH with increased amino acid-stimulated insulin secretion. Objectives: To study the genotype–phenotype correlations in patients with GLUD1 mutations. To report the phenotype and functional analysis of a novel mutation (P436L) in the GLUD1 gene associated with the absence of HA. Patients and methods: Twenty patients with HI from 16 families had mutational analysis of the GLUD1 gene in view of HA (n=19) or leucine sensitivity (n=1). Patients negative for a GLUD1 mutation had sequence analysis of the SIRT4 gene. Functional analysis of the novel P436L GLUD1 mutation was performed. Results: Heterozygous missense mutations were detected in 15 patients with HI/HA, 2 of which are novel (N410D and D451V). In addition, a patient with a normal serum ammonia concentration (21 µmol/l) was heterozygous for a novel missense mutation P436L. Functional analysis of this mutation confirms that it is associated with a loss of GTP inhibition. Seizure disorder was common (43%) in our cohort of patients with a GLUD1 mutation. No mutations in the SIRT4 gene were identified. Conclusion: Patients with HI due to mutations in the GLUD1 gene may have normal serum ammonia concentrations. Hence, GLUD1 mutational analysis may be indicated in patients with leucine sensitivity; even in the absence of HA. A high frequency of epilepsy (43%) was observed in our patients with GLUD1 mutations

Long-term results of mitral valve repair for myxomatous disease with and without chordal replacement with expanded polytetrafluoroethylene sutures

AbstractObjective: This study was carried out to evaluate the long-term results of mitral valve repair for mitral regurgitation caused by myxomatous disease of the mitral valve and the late effects of chordal replacement with expanded polytetrafluoroethylene sutures in this operation. Methods: A total of 324 patients with mitral regurgitation caused by myxomatous disease underwent mitral valve repair from 1981 to 1995; the group comprised 241 men and 83 women whose mean age was 58 ± 14 years. Chordal replacement with expanded polytetrafluoroethylene sutures has been performed in 165 patients since 1985. Most of the patients who had chordal replacement with expanded polytetrafluoroethylene sutures had prolapse of the anterior leaflet or prolapse of both leaflets, whereas most patients who had mitral valve repair without chordal replacement had prolapse of the posterior leaflet. Patients were followed up at annual intervals and had a Doppler echocardiographic study. The follow-up was complete and extended from 6 to 156 months (mean 36 ± 30 months). Results: Two operative and 21 late deaths occurred (14 cardiac and 7 noncardiac). At 10 years the actuarial survival was 75% ± 5%, the freedom from stroke was 94% ± 2%, the freedom from transient ischemic attacks was 92% ± 4%, the freedom from endocarditis was 99% ± 1%, the freedom from mitral valve reoperation was 96% ± 1%, and the freedom from severe mitral regurgitation was 93% ± 3%. Chordal replacement with expanded polytetrafluoroethylene sutures had no effect on any of these end points. Conclusions: Mitral valve repair was feasible in most patients with mitral regurgitation caused by myxomatous disease and it was associated with low rates of valve-related complications. Chordal replacement with expanded polytetrafluoroethylene had no adverse effect on the late outcome and was believed to have increased the probability of mitral valve repair. (J Thorac Cardiovasc Surg 1998;115:1279-86

Detection of serum prostate specific antigen in lactating, pregnant, and advanced breast cancer Sudanese Women.

Introduction: Although prostate-specific antigen (PSA) is the most valuable tumor marker for the diagnosis and management of prostate carcinoma, it is widely accepted that PSA is not prostate specific.Objectives: The aim of this study is to address the possibility of using the PSA as marker for the sex assignment in different categories and relevance of this test in women problems.Method: We have evaluated the measurement of serum total PSA for differentiation between Sudanese women with advanced breast cancer (n= 10), and those are lactating (n=10), pregnant (n=10) compared with 20 healthy women as control group. Serum total PSA (TPSA) was measured using immuno-radiometric assay (IRMA).Results: In this study the mean age was significantly higher advanced breast cancer groups compared with lactating group (

A probabilistic multi-objective approach for FACTS devices allocation with different levels of wind penetration under uncertainties and load correlation

This study presents a probabilistic multi-objective optimization approach to obtain the optimal locations and sizes of static var compensator (SVC) and thyristor-controlled series capacitor (TCSC) in a power transmission network with large level of wind generation. In this study, the uncertainties of the wind power generation and correlated load demand are considered. The uncertainties are modeled in this work using the points estimation method (PEM). The optimization problem is solved using the Multi-objective particle swarm optimization (MOPSO) algorithm to find the best position and rating of the flexible AC transmission system (FACTS) devices. The objective of the problem is to maximize the system loadability while minimizing the power losses and FACTS devices installation cost. Additionally, a technique based on fuzzy decision-making approach is employed to extract one of the Pareto optimal solutions as the best compromise one. The proposed approach is applied on the modified IEEE 30-bus system. The numerical results evince the effectiveness of the proposed approach and shows the economic benefits that can be achieved when considering the FACTS controller

Bart Syndrome with Ear Malformation

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