One-sided and two-sided Green's functions

We discuss the one-sided Green's function, associated with an initial value problem and the two-sided Green's function related to a boundary value problem. We present a specific calculation associated with a differential equation with constant coefficients. For both problems, we also present the Laplace integral transform as another methodology to calculate these Green's functions and conclude which is the most convenient one. An incursion in the so-called fractional Green's function is also presented. As an example, we discuss the isotropic harmonic oscillator.

Transitions from reproductive systems governed by two self-incompatible Loci to one in fungi.

Self-incompatibility (SI), a reproductive system broadly present in plants, chordates, fungi, and protists, might be controlled by one or several multiallelic loci. How a transition in the number of SI loci can occur and the consequences of such events for the population's genetics and dynamics have not been studied theoretically. Here, we provide analytical descriptions of two transition mechanisms: linkage of the two SI loci (scenario 1) and the loss of function of one incompatibility gene within a mating type of a population with two SI loci (scenario 2). We show that invasion of populations by the new mating type form depends on whether the fitness of the new type is lowered, and on the allelic diversity of the SI loci and the recombination between the two SI loci in the starting population. Moreover, under scenario 1, it also depends on the frequency of the SI alleles that became linked. We demonstrate that, following invasion, complete transitions in the reproductive system occurs under scenario 2 and is predicted only for small populations under scenario 1. Interestingly, such events are associated with a drastic reduction in mating type number.

Role of the NALP3 Inflammasome in the Development of Two-Kidney, One Clip Hypertension in Mice

Objective: The NALP3 inflammasome functions as a sensor of danger signals and triggers processing and release of IL-1b. Mutations of NALP3 are responsible for the cryopyrin associated periodic syndromes, a group of autoinflammatory disorders that respond to IL1 inhibition. Genetic studies have also linked NALP3 to hypertension in man, but the mechanism is not understood. The aim of this study is to investigate the role of NAPL3 inflammasome in the development of hypertension in an animal model. Design and Method: Six-week old male WT and NALP3 KO mice were used for generating a two-kidney, one clip (2K1C) renovascular hypertension. A U-shaped stainless steel clip (O^ ¼0.12mm) was placed on left renal artery under anaesthesia. The same surgery without clipping was performed in sham mice. At week 6 and 12 after the clipping, intra-arterial blood pressure (BP) was measured in conscious mice. Blood was collected for plasma renin analysis. Heart and kidney were excised and stored for molecular and morphological examinations. n¼5-6 mice per group. Data are mean_SEM. Results: Mean BP was significantly increased at week 6 and 12 in WT-2K1C mice compared to WT-sham group (MBPweek6: 138_2 vs.124_3 mmHg, p<0.01 and MBPweek12: 141_5 vs.122_3 mmHg, p<0.01) followed with an significant increase in heart weight (HW) and a decrease in clipped kidney weight indices in WT-2K1C mice compared to the WT-sham (HW/ BWweek6: 4.65_0.04 vs. 3.99_0.12 mg/g, p<0.001 and HW/BWweek12: 4.94_0.15 vs. 4.22_0.12 mg/g, p<0.001). Interestingly, NALP3 KO-2K1C mice did not develop hypertension. The MBP of KO-2K1C mice was comparable to the KO-sham (MBPweek6: 122_3 vs. 119_3 mmHg, p>0.05 and MBPweek6: 128_5 vs.122_4 mmHg, p>0.05). There was also no significant change in heart and kidney weight indices between KO- 2K1C and KO-sham mice. Conclusion: The preliminary results suggest that absence of NALP3 protects mice from the development of renin-dependent hypertension. Further molecular and morphological examinations are ongoing for the confirmation and mechanism explanation.

Reduction of two functional gamma-globin genes to one: an evolutionary trend in New World monkeys (infraorder Platyrrhini).

Nucleotide sequences were determined for the gamma1- and gamma2-globin loci from representatives of the seven anciently separated clades in the three extant platyrrhine families (Atelidae, Pitheciidae, and Cebidae). These sequences revealed an evolutionary trend in New World monkeys either to inactivate the gamma1 gene or to fuse it with the gamma2 gene, i.e. to have only one functional fetally expressed gamma gene. This trend is clearly evident in six of the seven clades: (i) it occurred in atelids by deletion of most of the gamma1 gene in the basal ancestor of this clade; (ii-iv) in pitheciid titi, saki, and cebid capuchin monkeys by potentially debilitating nucleotide substitutions in the proximal CCAAT box of the gamma1 promoters and (v and vi) in cebid owl and squirrel monkeys by crossovers that fused 5' sequence from gamma1 with 3' sequence from gamma2. In the five clades with gamma1 and gamma2 loci separated by intergenic sequences (the fifth clade being the cebid marmosets), the gamma2 genes retained an unaltered proximal CCAAT motif and their gamma2 promoters accumulated fewer nucleotide substitutions than did the gamma1 promoters. Thus, phylogenetic considerations indicate that the stem platyrrhines, ancestral to all New World monkeys, had gamma2 as the primary fetally expressed gamma gene. A further inference is that when the earlier stem anthropoid gamma gene duplicated, gamma2 (at its greater downstream distance from epsilon) could evade embryonic activation by the locus control region but could be fetally activated once released by regulatory mutations from fetal repressors.

Dr. A.L. Crelle's calculating tables giving the products of every two numbers from one to one thousand and their application to the multiplication and division of all numbers above one thousand.

Mode of access: Internet.

Calculating tables, giving the products of every two numbers from one to one thousand and their application to the multiplication and division of all numbers above one thousand.

Added t.-p. in French and German. 9. ed 1904. p. III-X in French and German in parallel columns.

An historical sketch of the First Church in Boston, from its formation to the present period. To which are added two sermons, one on leaving the old, and the other on entering the new house of worship.

Mode of access: Internet.

Laws of the commonwealth of Pennsylvania, : from the seventh day of December, one thousand eight hundred and two, to the fourth day of April, one thousand eight hundred and five. : Re-published, under the authority of the legislature, by John Bioren. : Vol. VII.

"Errata."--p. [578].

A direction for ** adventvrers ** With small stock to get two for one.

Mode of access: Internet.

Comparison of two mentoring programs for at -risk Black adolescents: A traditional one -to -one mentoring program and a school -to -work transitional program

The purposes of this study were: (a) to compare the impact of One-to-One (OTO) mentoring interventions administered in the high school setting, and the workplace of the students who participated in the School-to-Work (STW) transitional program, and (b) to identify how the participants perceived their experience in the OTO mentoring program and the STW transitional program. A qualitative approach was used to identify how participants perceived their mentoring experiences with the STW and OTO mentoring programs by utilizing focus groups and content analysis. A quantitative approach was used to compare the statistical differences of outcomes between the STW and OTO mentoring programs, by utilizing descriptive statistics, independent samples t-tests, chi-square analyses, and logistic regression. The sample was limited to participants in the STW and OTO mentoring programs resulting in 21 participants for the qualitative approach and 114 participants for the quantitative approach. ^ Results from the qualitative approach indicated that focus group participants in the STW program were satisfied with the program and the relationship with their mentors. They also suggested that the STW program be lengthened to include the entire academic year. Participants from the OTO focus group were dissatisfied with their program due to inadequate mentor involvement. Results from the quantitative approach showed that the increase in school attendance for the STW program's at-risk Black male youth was statistically significant compared to the OTO program participants; the STW program participants displayed a better outlook for attending college that was statistically significant compared to those in the OTO program; and the OTO program participants displayed a better outlook for permanent employment compared to those in the STW program. ^ Therefore, this study finds that mentoring can contribute to reducing school absences and high school completion in order for at-risk Black adolescents to attend college. It is recommended that the OTO program be restructured to eliminate the disparity that exists regarding the administration of the STW program and the OTO program. ^

Application of standard and refined heat balance integral methods to one-dimensional Stefan problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

Traumatic recurrent anterior dislocation of the shoulder: two- to four-year follow-up of an anatomic open procedure.

The purpose of this study was to evaluate the results of an anatomic open stabilization procedure. Twenty-three consecutive patients with traumatic, recurrent, anterior glenohumeral instability were managed with a modified open procedure. All had a Bankart lesion. A standardized, true anatomic capsulolabral reconstruction was performed with suture anchors. Two patients were lost to follow-up, and twenty-one were evaluated after 36 months [range, 24-49 months] by an independent observer. Shoulder stability and function were the principal outcome measures. None of the patients had subsequent dislocations. All returned to full working capacity, and 19 reached their previous level of sport activities. The mean loss in active abduction and flexion was 1 degrees, in internal rotation, one vertebral level, and in external rotation, 7 degrees (arm at 90 degrees of abduction). Two patients had a positive anterior apprehension test. No sign of shoulder osteoarthritis was observed. The open anatomic capsulolabral reconstruction provides excellent results and allows the restoration of stability with good function.