Let p be a fixed odd prime number. Throughout this paper, Zp, Qp and Cp will denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers and N = N ∪ {0}. The p-adic norm is normally defined by |p|p = 1/p. As an indeterminate, we assume that q ∈ Cp with |1 − q|p < 1 (see [1-43]...

Three sulfated glycoproteins (ZP-1, ZP-2, and ZP-3) make up the zona pellucida, an extracellular glycocalyx that surrounds mouse oocytes. We have produced five monoclonal antibodies specific to the zona. All five immunoprecipitated ZP-2, and in addition, two of the antibodies immunoprecipitated ZP-3. This suggests the presence of either a common antigenic site or one made up in part by each of ...

BACKGROUND The zona pellucida (ZP), the mammalian oocyte coat, consists of a restricted number of highly glycosylated proteins. In vitro sperm binding studies suggest a higher binding affinity for the outer region of the ZP compared to its inner region in different species. However, the reason for this difference in binding distribution remains unresolved. Many studies suggest that the carbohyd...

Let p be a fixed prime number. Throughout this paper, the symbols Z, Zp, Qp, and Cp denote the ring of rational integers, the ring of p-adic integers, the field of p-adic rational numbers, and the completion of algebraic closure ofQp, respectively. LetN be the set of natural numbers andZ N∪{0}. Let νp be the normalized exponential valuation ofCp with |p|p p−νp p p−1. Let UD Zp be the space of u...

Let p be a fixed prime number. Throughout this paper, the symbols Z, Zp, Qp, and Cp denote the ring of rational integers, the ring of p-adic integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers. The normalized valuation in Cp is denoted by | · |p with |p|p 1/p. Let UD Zp be the space of uniformly differe...

The MAC construction that we saw in the previous lecture was not very practical in the sense that we can improve the construction by using the same key and tag length as before but for a bigger message space. That is, for some prime p we have: • K = Zp × Zp • M = Zp for some d ≥ 1 • T = Zp (We can replace Zp by any finite field F. In particular, it’s useful to use a binary extension field F2` s...

The zona pellucida (ZP) is an extracellular membrane surrounding mammalian oocytes. The so-called zona hardening plays a key role in fertilization process, as it blocks polyspermy, which may also be caused by an increase in the mechanical stiffness of the ZP membrane. However, structural reorganization mechanisms leading to ZP's biomechanical hardening are not fully understood yet. Furthermore,...

Polyspermy is a common problem in bovine in vitro fertilization (IVF) and has a still unclear etiology. In this specie, after IVF, despite the lack of a biochemical post-fertilization hardening, the stiffness of the outer ZP layer is significantly increased. Therefore, polyspermy might be related to an incomplete or insufficient stiffening of the ZP. We obtained, by using atomic force spectrosc...

Monospermy occurs in the process of normal fertilization where a single sperm fuses with egg, resulting formation diploid zygote. During fertilization, must penetrate zona pellucida (ZP), outer layer to reach egg’s plasma membrane. Once binds ZP, it undergoes an acrosomal reaction, which involves release enzymes from sperm's acrosome that help ZP. Ovastacin is one involved breaking down Studies...

Objective Apigenin is a plant-derived compound belong to the flavonoids category and has the protective effects on different cells. The aim was to evaluate the effect of apigenin on the number of viable and apoptotic blastomeres, the zona pellucida (ZP) thickness and the hatching rate of preimplantation mouse embryos exposed to H2O2 and actinomycin D. MaterialsAndMethods 420 two-cell embryos we...