THEORETICAL STUDY OF THE KINEMATIC AND DYNAMIC CHARACTERISTICS OF THE AUGER WORKING BODY OF A FOREST FIRE GROUND-THROWING MACHINE

The paper presents the results of studies of the working processes of screw working bodies in various industries. Studies of the technological parameters of screw working bodies during the removal of the ground cover with combustible plant residues have been insufficiently carried out. A new design of a forest fire machine is proposed, including screw working bodies for removing the ground cover with combustible plant residues, cut-out discs, for the formation of a soil shaft in front of the rotor-thrower, with an adjustable guide casing with the ability to change the directional flow of soil. Working bodies of the forest fire soil-throwing machine are described by a system of differential equations of the translational, rotational movements of the auger working body and the equation of the flow rates of the working fluid. The Cauchy problem is considered on the interval t∈ (t_0; t_end). Original system is reduced to a system of recurrence relations due to its nonlinearity, replacing the derivatives of the desired functions with their finite analogs. This system is unresolved with respect to the senior member. One can apply the method of splitting the system into systems in subspaces of decreasing dimensions and solve the system in these subspaces due to the Fredholm property of the operator coefficient in front of the leading term. The analytical solution of the mathematical model for removing the ground cover by auger working bodies of a forest fire soil-throwing machine when laying fire strips and extinguishing grassland forest fires makes it possible to determine the kinematic and dynamic parameters of the auger working bodies using the final formulas. Simulation modeling of the screw working process was carried out on a virtual laboratory bench. The dependences of the dynamic characteristics of the auger working bodies when overcoming obstacles have been obtained. It was found that the maximum average value of the torque is observed when overcoming an obstacle with a height of 100 mm and the rotation speed of the working body of 400 rpm is 1468.49 N ∙ m, at which its performance is not impaired.

Exponentially convergent method for an abstract integro - differential equation with fractional Hardy - Titchmarsh integral

A homogeneous fractional-differential equation with a fractional Hardy—Titchmarsh integral and an unboun-ded operator coefficient in a Banach space is considered. The conditions for the representation of the solution in the form of a Danford—Cauchy integral are established, and an exponentially convergent approximation method is developed.

Coefficient inequalities for certain classes of analytic function using q−derivatives

We introduce and we study certain classes of analytic functions which are defined by making use of the q-derivative operator. Coefficient inequalities for functions in these classes are discussed. Some interesting consequences of the results are also pointed out.

Bounded solutions of a difference equation with finite number of jumps of operator coefficient

We study the problem of existence of a unique bounded solution of a difference equation with variable operator coefficient in a Banach space. There is well known theory of such equations with constant coefficient. In that case the problem is solved in terms of spectrum of the operator coefficient. For the case of variable operator coefficient correspondent conditions are known too. But it is too hard to check the conditions for particular equations. So, it is very important to give an answer for the problem for those particular cases of variable coefficient, when correspondent conditions are easy to check. One of such cases is the case of piecewise constant operator coefficient. There are well known sufficient conditions of existence and uniqueness of bounded solution for the case of one jump. In this work, we generalize these results for the case of finite number of jumps of operator coefficient. Moreover, under additional assumption we obtained necessary and sufficient conditions of existence and uniqueness of bounded solution.

Effects of additional neck cut of the femur on the range of motion in total hip arthroplasty for hip dislocation: a computer simulation study

Background: Subtrochanteric shortening osteotomy (SSO) is commonly performed in total hip arthroplasty (THA) for high hip dislocation. However, this procedure is technically difficult and includes complications. Additional neck cut (ANC) of the femur is a procedure that involves femoral shortening by possibly eliminating the need for SSO in THA for high hip dislocation. Herein, we evaluated the effect and the depth limit of ANC of the femur on the range of motion (ROM) in THA for high hip dislocation. Methods: ROM was measured in 26 patients with high hip dislocation using computer software. The stem was deeply positioned at 5-mm intervals from 0 mm to 30 mm (7 groups). The ROM before impingement was measured during flexion, internal rotation (IR) at 90° flexion, external rotation (ER) and abduction. Receiver operator coefficient (ROC) curves for abduction were generated. The cut-off value of ANC where the required ROM was achieved was also determined. Results: Deeper ANCs increased the ROM values during flexion and IR, but they decreased the ROM values during ER and abduction. The ROM values during ER were also limited in 0-mm ANCs. According to the result of the ROC curve for abduction, 15 mm was considered as the permissible range of ANC. Conclusions: In THA for high hip dislocation additional neck cut should be taken into consideration for hips requiring less than 15-mm shortening. For more extended corrections a subtrochanteric shortening osteotomy should be performed.

Weighted Estimates of the Cayley Transform Method for Abstract Differential Equations

We represent the solution {u(t)} of an initial value problem (IVP) for the first-order differential equation with an operator coefficient as a series using the Cayley transform of the corresponding operator coefficient and the Laguerre polynomials. In the case of a boundary value problem (BVP) for the second-order differential equation with an operator coefficient, we represent its solution using the Cayley transform and the Meixner-type polynomials. The approximate solution is the truncated sum of N (the discretization parameter) summands. We give the error estimate of these approximations depending on N and the distance of t to the initial point of the time interval or of the spatial argument x to the boundary of the spatial domain.

Posterior sloping angle of the capital femoral physis in slipped capital femoral epiphysis has poor clinical utility and should not guide treatment on prophylactic fixation

Background: Prophylactic pinning of the uninvolved side after unilateral slipped capital femoral epiphysis (SCFE) is controversial as it balances increased surgical risks against the possibility of protecting a normal hip from initial slip and deformity. A posterior sloping angle (PSA) of greater than 12–14.5° has been proposed by various authors as a treatment threshold to predict for contralateral hip progression and prophylactic pinning. Methods: A retrospective review of a 10-year series of patients with the diagnosis of SCFE and follow-up of 18 months was conducted. Patients were divided into two groups, those with Isolated Unilateral Slips and those who subsequently underwent Subsequent Contralateral Progression. PSA measurements were performed by two clinicians and assessed for inter-observer reliability. Data collected included age, sex, ethnicity, Loder class, endocrinopathy, renal impairment, radiation exposure, and PSA. Results: There were no significant differences between the distribution of gender, site of slip, age of onset, Loder class, and presence of medical comorbidities between the Isolated Unilateral Slip and Subsequent Contralateral Progression groups ( p > 0.05). The mean PSA value was not significantly higher in the Subsequent Contralateral Progression group (17.9 ± 4.32 (10.5–23.5)) compared to the Isolated Unilateral Slip group (15.8 ± 5.31 (6–26)) ( p = 0.32). The receiver operator coefficient-derived ideal treatment threshold of 16.5° gave a sensitivity of 0.71, specificity of 0.64, and number needed to treat of 3. Conclusion: PSA differences between the Subsequent Contralateral Progression and Isolated Unilateral Slip groups were not statistically significant in this series. All proposed treatment thresholds had poor specificity. Prophylactic pinning should not be based on isolated PSA values. Level of evidence: III.