An Iterative Method for Solving Split Monotone Variational Inclusion Problems and Finite Family of Variational Inequality Problems in Hilbert Spaces

The purpose of this paper is to study the convergence analysis of an intermixed algorithm for finding the common element of the set of solutions of split monotone variational inclusion problem (SMIV) and the set of a finite family of variational inequality problems. Under the suitable assumption, a strong convergence theorem has been proved in the framework of a real Hilbert space. In addition, by using our result, we obtain some additional results involving split convex minimization problems (SCMPs) and split feasibility problems (SFPs). Also, we give some numerical examples for supporting our main theorem.

Neighborhoods and Manifolds of Immersed Curves

We present some fine properties of immersions ℐ : M ⟶ N between manifolds, with particular attention to the case of immersed curves c : S 1 ⟶ ℝ n . We present new results, as well as known results but with quantitative statements (that may be useful in numerical applications) regarding tubular coordinates, neighborhoods of immersed and freely immersed curve, and local unique representations of nearby such curves, possibly “up to reparameterization.” We present examples and counterexamples to support the significance of these results. Eventually, we provide a complete and detailed proof of a result first stated in a 1991-paper by Cervera, Mascaró, and Michor: the quotient of the freely immersed curves by the action of reparameterization is a smooth (infinite dimensional) manifold.

On the Determinants of the Square-Type Stirling Matrix and Bell Matrix

We study determinants of the square-type Stirling matrix S ∗ and the square-type Bell matrix B ∗ . For this purpose, we prove that S ∗ and B ∗ have LU factorizations S ∗ = L S U S and B ∗ = L B U B where the diagonal entries of U S are k k − 1 , while those of U B are k ! ( k ≥ 1 ).

Catalan Transform of k -Balancing Sequences

In this work, the Catalan transformation (CT) of k -balancing sequences, B k , n n ≥ 0 , is introduced. Furthermore, the obtained Catalan transformation C B k , n n ≥ 0 was shown as the product of lower triangular matrices called Catalan matrices and the matrix of k -balancing sequences, B k , n n ≥ 0 , which is an n × 1 matrix. Apart from that, the Hankel transform is applied further to calculate the determinant of the matrices formed from C B k , n n ≥ 0 .

Dynamical Modelling of Bone Formation and Resorption under Impulsive Estrogen Supplement: Effects of Parathyroid Hormone and Prolactin

Osteoporosis, a bone metabolic disease, is one of the major diseases occurring in aging population especially in postmenopausal women. A system of impulsive differential equations is developed in this paper in order to investigate the effects of parathyroid hormone and prolactin on bone-forming cells, namely, osteoblasts, and bone-resorbing cells, namely, osteoclasts, under the impulsive estrogen supplement. The theoretical analysis of the developed model is carried out so that we obtain the conditions on the system parameters in which the stability and permanence of the model can occur. Computer simulations are also provided to illustrate the theoretical predictions.

The Mechanical Behavior of a Multispring System Revealing Absurdity in the Relativistic Force Transformation

The mechanical motion of a system consisting of simple springs is investigated from the viewpoint of two inertial observers with a relativistic relative velocity. It is shown that the final displacement of the springs is not measured the same by the observers. Indeed, it is demonstrated that there is an incompatibility between kinematics and dynamics in Einstein’s relativity regarding the force transformation.

Some Random Fixed-Point Theorems for Weakly Contractive Random Operators in a Separable Banach Space

The aim of this paper is to prove a common random fixed-point and some random fixed-point theorems for random weakly contractive operators in separable Banach spaces. A random Mann iterative process is introduced to approximate the fixed point. Finally, the main result is supported by an example and used to prove the existence and the uniqueness of a solution of a nonlinear stochastic integral equation system.

Multivalent Functions Related with an Integral Operator

In this present paper, we introduce and explore certain new classes of uniformly convex and starlike functions related to the Liu–Owa integral operator. We explore various properties and characteristics, such as coefficient estimates, rate of growth, distortion result, radii of close-to-convexity, starlikeness, convexity, and Hadamard product. It is important to mention that our results are a generalization of the number of existing results in the literature.

The Log-Asset Dynamic with Euler–Maruyama Scheme under Wishart Processes

This article deals with Wishart process which is defined as matrix generalization of a squared Bessel process. We consider a single risky asset pricing model whose volatility is described by Wishart affine diffusion processes. The multifactor volatility specification enables this model to be flexible enough to describe the market prices for short or long maturities. The aim of the study is to derive the log-asset returns dynamic under the double Wishart stochastic volatility model. The corrected Euler–Maruyama discretization technique is applied in order to obtain the numerical solution of the log-asset return dynamic under Bi-Wishart processes. The numerical examples show the effect of the model parameters on the asset returns under the double Wishart volatility model.

Direction Curves Associated with Darboux Vectors Fields and Their Characterizations

In this paper, we consider the Darboux frame of a curve α lying on an arbitrary regular surface and we use its unit osculator Darboux vector D ¯ o , unit rectifying Darboux vector D ¯ r , and unit normal Darboux vector D ¯ n to define some direction curves such as D ¯ o -direction curve, D ¯ r -direction curve, and D ¯ n -direction curve, respectively. We prove some relationships between α and these associated curves. Especially, the necessary and sufficient conditions for each direction curve to be a general helix, a spherical curve, and a curve with constant torsion are found. In addition to this, we have seen the cases where the Darboux invariants δ o , δ r , and δ n are, respectively, zero. Finally, we enrich our study by giving some examples.