Circuit lengths of graphs for the Picard group

In this paper, we examine some properties of suborbital graphs for the Picard group. We obtain edge and circuit conditions, then propose a conjecture for the graph to be forest. This paper is an extension of some results in (Jones et al. in The Modular Group and Generalized Farey Graphs, pp. 316-338, 1991)

Representations by certain octonary quadratic forms whose coefficients are 1, 2, 3 and 6

WOS: 000330644800009We determine formulae for the numbers of representations of a positive integer by certain octonary quadratic forms whose coefficients are 1, 2, 3 and 6.Natural Sciences and Engineering Research Council of CanadaNatural Sciences and Engineering Research Council of CanadaCGIAR; Recep Tayyip Erdogan UniversityRecep Tayyip Erdogan University; Council of Higher Education of TurkeyMinistry of National Education - TurkeyThe authors are very grateful to Professor Ayse Alaca and Professor Emeritus Kenneth S. Williams for helpful discussions during the preparation of this paper. the research of the first author was supported by a research grant from the Natural Sciences and Engineering Research Council of Canada. the research was carried out during the second author's visit to Carleton University, Ottawa, Canada. He would like to thank Carleton University for the hospitality during his stay. He also thanks Recep Tayyip Erdogan University and the Council of Higher Education of Turkey for their financial support

Evaluation of the convolution sums Sigma(l+27m=n) sigma(l)sigma(m) and Sigma(l+32m=n) sigma(l)sigma(m)

WOS: 000369696700001We determine the convolution sums Sigma(l+27m= n) sigma(l)sigma(m) and Sigma(l+32m= n) sigma(l)sigma(m) for all positive integers n. We then use these evaluations together with known evaluations of other convolution sums to determine the numbers of representations of n by the octonary quadratic forms x(1)(2) + x(1)x(2) + x(2)(2) + x(3)(3) + x(3)x(4) + x(4)(2) + 9(x(5)(2) + x(5)x(6) + x(6)(2) + x(7)(2) + x(7)x(8) + x(8)(2)) and x(1)(2) + x(2)(2) + x(3)(2) + x(4)(2) + 8(x(5)(2) + x(6)(2) + x(7)(2) + x(8)(2)). A modular form approach is used.Scientific and Technological Research Council of Turkey (TUBITAK)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK)The research was carried out during the second author's visit to Carleton University, Ottawa, Canada. He would like to thank Carleton University for the hospitality during his stay. He also thanks the Scientific and Technological Research Council of Turkey (TUBITAK) for the financial support

Connectedness of a suborbital graph for congruence subgroups

In this paper, we give necessary and sufficient conditions for the graph Hu,n to be connected and a forest

Disconnectedness of the subgraph F-3 for the group Gamma(3)

WOS: 000325451500001In this paper we show that the subgraph F-3 is disconnected and that for all integers m, we find all integers a and b such that (9m(2) - 4)a(2) + 4 and 5b(2) +/- 4 are square. It turns out that the set of numbers b comprises the Fibonacci numbers

Suborbital graphs for the group ?2

In this paper, we investigate suborbital graphs formed by the action of?2which is the group generated by the second powers of the elementsof the modular group ? on ^Q. Firstly, conditions for being an edge,self-paired and paired graphs are provided, then we give necessary andsufficient conditions for the suborbital graphs to contain a circuit andto be a forest. Finally, we examine the connectivity of the subgraphFu,Nand show that it is connected if and only if N <=

The value of plasma SCUBE1 and oxidative stress parameters in the early diagnosis of acute ovarian torsion

Tokgoz, Vehbi Yavuz/0000-0002-4113-385XWOS: 000472479100009PubMed: 31223027AIM: The purpose of our study was to determine the diagnostic value of plasma SCUBE1, malondialdehyde (MDA), superoxide dismutase (SOD) and total antioxidant status (TAS) investigated on the 4th hour of ovarian torsion, and at the same time to determine the relation between these markers and histopathological damage occurring in the ovary. MATERIALS AND METHODS: Sixteen rats were included, eight in the torsion group and eight in the control group. The right ovaries of the rats in the torsion group were rotated clockwise 720 degrees, after which they were fi xed and attached to the abdominal wall. The abdominal walls of the control group rats were opened for 1 min and then closed. Relaparotomy was performed 4 h after surgery in both groups, blood specimens were collected for biochemical analyses, and the right ovaries were surgically extracted. RESULTS: No statistically signifi cant difference was determined in the control and torsion groups' plasma SCUBE1, SOD and TAS values (p = 0.987, p = 0.33, and p = 0.244, respectively). Torsion group plasma MDA values were signifi cantly higher than those of the control group (p = 0.039). At histopathological evaluation, histological score, apoptotic index and Caspase-3 index values of the torsion group were signifi cantly higher compared to the control group. CONCLUSION: Plasma SCUBE1 is not useful in the early diagnosis of ovarian torsion. Similarly, use of the oxidative stress markers SOD and TAS does not appear useful in early diagnosis, although MDA may be considered for that purpose (Tab. 2, Fig. 3, Ref. 23). Text in PDF www.elis.sk.Scientific Research Committee of Giresun University [100517-125]The study was supported by the Scientific Research Committee of Giresun University (100517-125)

A new approach to prevent ischemia/reperfusion injury in a rat model: remote ischemic conditioning

sipahi, mehmet/0000-0001-8344-9863WOS: 000468754900021PubMed: 30980277Purpose To evaluate the effect of remote ischemic conditioning (RIC) on ovarian ischemia/reperfusion injury in a rat model. Methods A total of 36 Wistar albino rats with a body weight of 220-250 g were used for this study. Right adnexal torsion was performed for 180 min, and at the end of the period, the adnex was released and the abdomen was reclosed for 180 min for reperfusion. Torsion and detorsion procedures were applied to all rats except group 1 (sham, control). The right lower extremity was tied to perform remote tissue ischemia in groups 3, 4, 5, and 6. The goal of the procedure, which was purplish discoloration and pulselessness of the extremity, was maintained. After 5 min of ischemia, reperfusion was achieved for 5 min. Repeating this procedure 3 times was defined as hypoxia attacks (RIC). Retrieved ovaries were examined for tissue injury with biochemical, histopathologic, and immunohistochemical analysis. Results Unlike the control group, vascular congestion, hemorrhage, edema, and inflammatory cell infiltration were observed in group 2 (only I/R [ischemia/reperfusion]). In groups 3 (I/R + RIC), 4 (I/R + RIC), 5 (I/R + RIC), and 6 (I/R + RIC), edema and inflammatory cell infiltration were not observed. However, vascular congestion and hemorrhage that were detected in these groups were higher than in group 1 (Control) and less than in group 2 (I/R). The Caspase-3 Index was found to be increased in all groups compared to group 1 (P < .001). However, the increase in the RIC-performed groups was significantly less than in group 2. The apoptotic index, which was determined by the TUNEL, was also found to be increased in all groups compared to group 1 (P < .001). When the comparison was made in relation to group 2, the decrease of AI in RIC-performed groups was statistically significant, except the decrease in group 6 (P = .29). Conclusions It is not clinically conceivable to prepare the tissue for pre-ischemia in ovarian torsion. However, the RIC application, which will be initiated if torsion is suspected when arrangements are made for surgery, might be a simple, effective, and inexpensive approach to prevent I/R injury in the clinic.Giresun University BAP Committee [SAG-BAP-A-160317-87]The study was supported by the Giresun University BAP Committee (SAG-BAP-A-160317-87)