A Subclass of Janowski Starlike Functions Involving Mathieu-Type Series

To date, many interesting subclasses of analytic functions involving symmetrical points and other well celebrated domains have been investigated and studied. The aim of our present investigation is to make use of certain Janowski functions and a Mathieu-type series to define a new subclass of analytic (or invariant) functions. Our defined function class is symmetric under rotation. Some useful results like Fekete-Szegö functional, a number of sufficient conditions, radius problems, and results related to partial sums are derived.

Subclasses of Uniform Univalent Functions Associated with Srivastava and Attiya Operator

In this paper, we introduce new subclasses k−STs(p,β) and k−UKs(p,β) of analytic and univalent functions in the canonical domain associated with the Srivastava and Attiya operator. The radius problems of these subclasses regarding symmetrical points are investigated and compared with previous known results. Certain properties and conditions of these subclasses such as integral representation are also discussed in this work.

On Bessel Functions Related with Certain Classes of Analytic Functions with respect to Symmetrical Points

In the present investigation, subclasses of analytic functions with respect to symmetrical points which are defined by the generalized Bessel functions of the first kind of order μ are introduced. Furthermore, some alluring geometric properties of these classes, which include inclusion property, integral-preserving properties, coefficients, and distortion results are studied. Moreover, some consequences of our results are also given.

ASSESSMENT OF BONE QUALITY IN THE FRONTAL PART OF MANDIBLES IN FEMALE PATIENTS OF VARIOUS AGES USING CONE-BEAM COMPUTED TOMOGRAPHY

Thing. The optical density of the lower jaw in the frontal part of female patients was studied, age-related differences in the optical density of the lower jaw were revealed. The aim is to reveal the variability of the values of optical density of the lower jaw in the anterior region in female patients. Methodology. Computed tomograms of the lower jaws of 26 patients were analyzed. The optical density of the bone was assessed using the method of computer densitometry in Hounsfield arbitrary units, measurements were carried out in the area of the root apexes of the lower canines. Statistical analysis was carried out using Microsoft Excel, Windows 9. Results. In 84.6 % of cases, the optical density of bone tissue in the area of 3.3 and 4.3 teeth is within the same class according to the Misch classification. In this group, 72.7 % of patients had class D2, 18.18 ― D1, 9 ― D3; in 15.4 %, the bone density on the right and left sides of the mandible belongs to D2 and D3. The optical density between two relatively symmetrical points is in the range from 2 to 238 units, between the right and left sides it is 129.66 HU. In the group of 30―39 (n = 6) years, in 50 % of cases, bone density belongs to class D2, in 33.33 ― D1, in 16.66 ― D3; 40―49 (n = 8) years in 87.5 % of cases ― D2, in 12.5 ― D1; 50―59 (n = 6) years at 50 % ― D2 and at 50 ― D3; 60―68 (n = 6) years at 50 % ― D2 and at 50 ― D3. Conclusions. With increasing age of patients, there is a decrease in bone density in the lower jaw in the canine area.

On the application of the theory of dissociation of electrolyte solutions of Arrenius to electrophysiology

It is known that if we make a transverse cut of the muscle at a right angle to its axis, then the points located at an equal distance and symmetrical with respect to the center of the cut surface will have the same potentials, and therefore, when we move away from these places, we will not receive any current; if the cut is made with a greater or lesser sharp angle, then when two symmetrical points of such a transverse cut are retracted, one of which is closer to the obtuse one and the other to the acute angle, the current is obtained, and it turns out that the place lying at the obtuse angle is always positively in relation to lying in acute. These currents are called tilt currents.

Spacecraft Pose Estimation Based on Different Camera Model

Spacecraft pose estimation is an important technology for spacecraft to maintain or change its orientation in space. For spacecraft pose estimation, when two spacecraft are relatively far away, the depth information of the space point is less than that of measuring distance, so that the camera model can be seen as a weak perspective projection model. In this paper, a spacecraft pose estimation algorithm based on four symmetrical points of the spacecraft outline is proposed. Analytical solution of spacecraft pose is obtained by solving the weak perspective projection model, which can meet the requirements of the measurement model when there is a long measurement distance. Optimal solution is obtained from the weak perspective projection model to the perspective projection model, which can meet the measurement requirement when the measuring distance is close. The simulation results show that the proposed algorithm can get better results even though the noise is large.

Fekete-Szegö Type Problems and Their Applications for a Subclass of q-Starlike Functions with Respect to Symmetrical Points

In this article, by using the concept of the quantum (or q-) calculus and a general conic domain Ω k , q , we study a new subclass of normalized analytic functions with respect to symmetrical points in an open unit disk. We solve the Fekete-Szegö type problems for this newly-defined subclass of analytic functions. We also discuss some applications of the main results by using a q-Bernardi integral operator.

Fuzzy Differential Subordinations Results for λ-pseudo Starlike and λ-pseudo Convex Functions with Respect to Symmetrical Points

In the present work, we establish some fuzzy differential subordination results for λ‑pseudo starlike and λ-pseudo convex functions with respect to symmetrical points in the open unit disk.

Strut Confinement of Simply Supports Deep Beam Using Strut Reinforcement

This study investigates the effect of confining the Strut region of the deep beam by using Struts Reinforcement; which consists of four main bars enclosed by stirrups. Six specimens were tested for investigating the behavior of deep beams including; ultimate load, mid-span deflection, crack pattern, first shear and first flexure cracks, concrete surface strain and mode of failure. The specimens were tested under two symmetrical points load with and of 1 and compressive strength of 38 MPa. The main parameters were: first one the diameter of the main bars of Strut Reinforcement (8, 10, 12 mm) with constant spacing of stirrups equal to 80 while the other parameter was varied spacing of stirrups of strut reinforcement (120, 100, and 80 mm) with constant main bars diameter of 8 mm. The test results showed that the Strut confinement generally increased the ultimate load from 750 kN to 1250 kN and the ductility of the beam, confined shear cracks and strain surface across the strut and shear area and turned failures mode from shear failure to flexure. The increase in the diameter of the main bars enhanced the behavior of the beam more than the stirrups number.

Some Janowski Type Harmonic q-Starlike Functions Associated with Symmetrical Points

The motive behind this article is to apply the notions of q-derivative by introducing some new families of harmonic functions associated with the symmetric circular region. We develop a new criterion for sense preserving and hence the univalency in terms of q-differential operator. The necessary and sufficient conditions are established for univalency for this newly defined class. We also discuss some other interesting properties such as distortion limits, convolution preserving, and convexity conditions. Further, by using sufficient inequality, we establish sharp bounds of the real parts of the ratios of harmonic functions to its sequences of partial sums. Some known consequences of the main results are also obtained by varying the parameters.