Geometry of Evolving Plane Curves Problem via Lie Group Analysis

The purpose of the present work is to construct new geometrical models for motion of plane curves. We have obtained nonlinear partial differential equations and have discussed the solutions of these equations using symmetry groups methods. Also, geometric interpretation for these solutions are given through the Gaussian and mean curvatures to the soliton surfaces attached to the solution of the evolving problem. Key Words: Motion of curve; Symmetry groups; Monge for

Weingarten timelike tube surfaces around a spacelike curve,

Abstract The subject of this paper is the study of a timelike tube surface around the spacelike curve with timelike and spacelike binormal vectors in a three-dimensional Minkowski space E 3 1 . Moreover, we have discussed Weingarten and linear Weingarten conditions for this surface with respect to their curvatures; the mean curvature H , Gaussian curvature K and the second Gaussian curvature K II

On Dual Curves of DAW(k)-Type and Their Evolutes

In this paper, we study to express the theory of curves including a wide section of Euclidean geometry in terms of dual vector calculus which has an important place in the three -dimensional dual space $\mathbb{D}^{3}$. In other words, we study $DAW(k)$-type curves $\left( 1\leq k\leq 3\right)$ by using Bishop frame defined as alternatively of these curves and give some of their properties in $\mathbb{D}^{3}$. \ Moreover, we define the notion of evolutes of dual spherical curves for ruled surfaces. Finally, we give some examples to illustrate our findings

Some Properties of Special Magnetic Curves

In the theory of curves, a magnetic field generates a magnetic flow whose trajectories are curves called magnetic curves. This paper aims at studying some properties for these curves which corresponding to the Killing magnetic fields in the 3-dimensional Euclidean space. We investigate the trajectories of the magnetic fields called $T$-magnetic and $e$-magnetic curves, also we give some characterizations of these curves. In addition, we determine all magnetic curves for new spherical images of a spherical curve and finally, we defray some examples to confirm our main results

Protective effect of garlic extract against maternal and foetal cerebellar damage induced by lead administration during pregnancy in rats

Background: In spite of its industrial usefulness and varied daily uses, lead (Pb) pollution is a widespread ecological problem that faces the humans in the 21th century. Pb was found to produces a wide range of toxic effects including neurotoxicity especially to the developing and young offspring. Recently, the utilisation of herbal plants has received a significant attention where there has been rising awareness in their therapeutic use; among these is the garlic. In light of the above, the current study is designed experimentally in female pregnant rats in order to investigate the beneficial role of garlic extract in the protection from the maternal and foetal cerebellar damage produced by administration of different doses of Pb during pregnancy. Materials and methods: Positively pregnant female rats were divided into five groups; one control group, two Pb-treated groups (exposed to 160 and 320 mg/kg b.w. of Pb, respectively) and two groups treated with both Pb and garlic (exposed to Pb as previous groups together with 250 mg/kg b.w./day of garlic extract). Treatments started from day 1 to day 20 of pregnancy, where the mother rats of different experimental groups were sacrificed to obtain the foetuses. Pb level in the maternal and foetal blood and cerebellum was estimated by spectrophotometry. Specimens of the cerebellum of different mother and foetal groups were processed to histological and immunohistochemical staining for microscopic examination. Results: The results showed that administration of Pb to pregnant rats resulted in a dose-dependent toxicity for both mothers and foetuses in the form of decrease in maternal weight gain, placental and foetal weights, brain weight and diminished foetal growth parameters, which were prominent in rat’s group treated with larger dose of Pb. In Pb-treated rats, Pb level in blood and cerebellum was high when compared with the control group. The histopathological examination of the cerebellum of treated dams and foetuses showed marked alterations mainly in the form of Purkinje cell degeneration and lack of development of foetal cerebellum. Co-treatment of garlic extract along with Pb resulted in a significant decrease in Pb levels as compared with those treated with Pb alone with improvement of the histopathological changes. Conclusions: This study was useful in evaluating the hazardous effects of uncontrolled use of Pb in general and in assessing the developmental and neurotoxicity of foetuses due to exposure during pregnancy in particular. Co-administration of garlic has beneficial effects in amelioration of Pb-induced neurotoxicity and reversing the histopathological changes of the cerebellum of mother rats and foetuses. (Folia Morphol 2018; 77, 1: 1–15

Protective immune responses against Schistosoma mansoni infection by immunization with functionally active gut-derived cysteine peptidases alone and in combination with glyceraldehyde 3-phosphate dehydrogenase

© 2017 Tallima et al. Background: Schistosomiasis, a severe disease caused by parasites of the genus Schistosoma, is prevalent in 74 countries, affecting more than 250 million people, particularly children. We have previously shown that the Schistosoma mansoni gut-derived cysteine peptidase, cathepsin B1 (SmCB1), administered without adjuvant, elicits protection (>60%) against challenge infection of S. mansoni or S. haematobium in outbred, CD-1 mice. Here we compare the immunogenicity and protective potential of another gut-derived cysteine peptidase, S. mansoni cathepsin L3 (SmCL3), alone, and in combination with SmCB1. We also examined whether protective responses could be boosted by including a third non-peptidase schistosome secreted molecule, glyceraldehyde 3-phosphate dehydrogenase (SG3PDH), with the two peptidases. Methodology/Principal findings: While adjuvant-free SmCB1 and SmCL3 induced type 2 polarized responses in CD-1 outbred mice those elicited by SmCL3 were far weaker than those induced by SmCB1. Nevertheless, both cysteine peptidases evoked highly significant (P < 0.005) reduction in challenge worm burden (54–65%) as well as worm egg counts and viability. A combination of SmCL3 and SmCB1 did not induce significantly stronger immune responses or higher protection than that achieved using each peptidase alone. However, when the two peptidases were combined with SG3PDH the levels of protection against challenge S. mansoni infection reached 70–76% and were accompanied by highly significant (P < 0.005) decreases in worm egg counts and viability. Similarly, high levels of protection were achieved in hamsters immunized with the cysteine peptidase/SG3PDH-based vaccine. Conclusions/Significance: Gut-derived cysteine peptidases are highly protective against schistosome challenge infection when administered subcutaneously without adjuvant to outbred CD-1 mice and hamsters, and can also act to enhance the efficacy of other schistosome antigens, such as SG3PDH. This cysteine peptidase-based vaccine should now be advanced to experiments in non-human primates and, if shown promise, progressed to Phase 1 safety trials in humans