The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

Quantum channels enable the achievement of communication tasks inaccessible to their
classical counterparts. The most famous example is the distribution of secret keys. Unfortunately, the rate
of generation of the secret key by direct transmission is fundamentally limited by the distance. This limit
can be overcome by the implementation of a quantum repeater. In order to boost the performance of the
repeater, a quantum repeater based on cut-off with two different types of quantum memories is suggestd,
which reduces the effect of decoherence during the storage of a quantum state.

Background: Change in palatal vault shape and Reinforcement of high impact acrylic denture base resin may in turn affect the dimensional accuracy of acrylic resin and affecting the fitness of the denture. The aim of study is to evaluate the effect of fiber reinforcement for high-impact acrylic resin denture base with different palatal vault shapes on linear dimensional change and effect of palatal vault shapes on linear dimensional changes of non-reinforced and fiber reinforced high impact denture base acrylic resin Material and method: Three different palatal vault shapes were prepared on standard casts using CNC (computer numerical control) machine. 60 samples of heat polymerized high impact acrylic resin maxillary denture base were fabri

Background: Change in palatal vault shape and Reinforcement of high impact acrylic denture base resin may in turn affect the dimensional accuracy of acrylic resin and affecting the fitness of the denture.This study evaluated tostudy the effect of fiber reinforcement for high-impact acrylic resin denture base with different palatal vault shapes on adaptation or gap space between the denture base and the stone cast and compare with non-fiber reinforcement and effect of palatal vault shapes on adaptation of non-reinforced and fiber reinforced high impact denture base acrylic resin Material and method: Three different palatal vault shapes were prepared on standard casts using CNC (computer numerical control) machine. 60 samples of heat polymeri

The aim of the research is to study the biology, life cycles, distribution and structure of the reproductive organ of Leucozonella retteri in natural conditions. Zoological and malacological methods are used in the work. The collection of the material was carried out according to A.A. Shileiko method. According to the results of the conducted studies, the differences between Leucozonella retteri and other species in the structure of the reproductive organ were manifested in the following. The lower part of the sperm is straight, the ovary is slightly curved. The paw pad is 8, located in 4x2 positions. The stylophore is large spherical. The vagina is cylindrical, its length is 5-6 times greater than the width. The penis is large and conve

Background: with the advent of new postmaterial in dentistry, it has become important to measure fitness of post restoration along the horizontal plane of the root space.This study aimed to measure and compare, the cement film thickness of conventional zinc phosphate cement in micrometer between the post and root dentin along horizontal plane at different post space regions (coronal, middle and apical) of four types of posts, by using stereomicroscopy. Material and methods: Thirty-two extracted human maxillary canines, mandibular canines and maxillary central incisors (n=32) were instrumented with ProTaper system files (hand use) and obturated with gutta-percha for ProTaper and AH26® root canal sealer. After 24hrs of incubation at 37ºC, p