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The cylindrical -- conical intersections are often met in technique as parts of pipes, tanks, bends etc. The paper work proposes a comparison between methods to solve the cylindrical -- conical intersection problems. The problems may be solved either applying graphical, descriptive geometry methods or using analytical methods. The graphical method uses a certain number of points to find the intersection curves and the development of the solids, the analytical method uses a complex enough mathematical apparatus. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence of radial solutions to a k-Hessian system in a general form. The existence of radial solutions is obtained under the assumptions that the nonlinearities in the given system satisfy k-superlinear, k-sublinear or k-asymptotically linear at the origin and infinity, respectively. The results presented in this paper generalize some known results. Examples are given for the illustration of the main results. [ABSTRACT FROM AUTHOR]

This paper discusses the existence of positive radial symmetric solutions of the nonlinear biharmonic equation ▵ 2 u = f (u , ▵ u) on an annular domain Ω in R N with the Navier boundary conditions u | ∂ Ω = 0 and ▵ u | ∂ Ω = 0 , where f : R + × R − → R + is a continuous function. We present some some inequality conditions of f to obtain the existence results of positive radial symmetric solutions. These inequality conditions allow f (ξ , η) to have superlinear or sublinear growth on ξ , η as | (ξ , η) | → 0 and ∞. Our discussion is mainly based on the fixed-point index theory in cones. [ABSTRACT FROM AUTHOR]

This paper discusses the existence of solutions to fourth order nonlinear boundary value problem involving systems of differential equations and two point boundary conditions. The nonlinearity f ∈ C([0, 1] × R+n × Rn × Rn × Rn, Rn) considered in this paper includes derivatives up to order three. Using recent fixed point results for the sum of two operators, we impose a growth condition on f to establish new existence criterion that ensure the existence of at least one and the existence of at least two nonnegative solutions. [ABSTRACT FROM AUTHOR]

One nappe of a right circular cone, cut by a transverse plane, splits the cone into an infinite frustum and a cone with an elliptical section of finite volume. There is a standard way of computing this finite volume, which involves finding the parameters of the so-called shadow ellipse, the characteristics of the oblique ellipse (the cut) and, finally, the projection of the vertex of the cone onto the oblique ellipse. This paper shows that it is possible to compute that volume just by using the information of the shadow ellipse and the height of the cone. Indeed, the finite slant cone has the same volume of an elliptic right cone, with the base being the shadow ellipse of the cut portion and with the height being the distance between the vertex of the cone and the intersection of the height of the original cone with the cutting plane. This is proved by introducing a volume-preserving shear transformation of the elliptical slant cone to a right cone, so that the standard volume formula for a cone can be straightforwardly applied. This implies a simplification in the procedure for computing the volume, since the oblique ellipse—i.e., the difficult part—can be neglected because only the shadow ellipse needs to be determined. [ABSTRACT FROM AUTHOR]

In this paper, we build four-part cone models to explore the coupling effect of seven cone fiber couplers. Moreover, this is the first study of the coupling effect of four layers of biological couplers in animals and other biological lives. We simulate the four layers cone couplers by using the beam propagation method, and we assume the input beam is located at the outer fiber of the central cone. Our simulation results showed that there are two wavelength regions (short and long wavelength regions) with the strongest coupling, where the most power of input optical powers of the central cones will transfer to the six surrounding cones after transmitting through the four layers of cone couplers. However, within a wavelength region of ±75 nm near to the peak wavelengths, located in the yellow–green wavelength range, the splitting ratios at the output of the outer segment of the central cone are always greater than the sum of the splitting ratios of the six surrounding cones. These cone couplers may play an important role in color preprocessing (e.g., doing opponent color processing partially). The cone fiber coupler effect and light absorption of cones are considered separately in our models. By taking account of both the cone fiber coupling effect and absorption of outer segment of L cone, we find the multiplication of the relative optical power of cone couplers, the spectral sensitivity data of the L cone, and a normalized coefficient that matches with the photopic luminous efficiency of the human eye well. This is the attempt to use both the cone fiber coupling effect and the absorption of L cones to explain the photopic luminous efficiency. The splitting ratios of the central cones are greater than 80% at peak wavelengths located in the yellow-green wavelength range, and this can help to explain why the human eye is more sensitive to green light. [ABSTRACT FROM AUTHOR]

This paper considers a class of fractional impulsive wave equations and improves a previous results. In fact, this paper adopts a new topological approach to prove the existence of classical solutions with a complex arguments caused by impulsive perturbations. To the best of our knowledge, there is a severe lack of results related to such impulsive equations. [ABSTRACT FROM AUTHOR]

This paper proposes a general definition of an undominated maximal of a relation on a constraint set. No specific requirement is imposed on either the asymmetry of the objective relation or the constraint set (which might, or might not, coincide with the ground set of the objective relation). Several characterizations are formulated that express undominated maximals of an objective relation as maximals of some trace associated with that objective relation. By means of some of these characterizations, the structure of the entire set of undominated maximals is examined in the particular case of relations induced by open and closed convex cones—among them, the weak and strong Pareto dominance—and, in the case of semiorders, that admit certain types of representability. The results of the last part of the examination allow the construction of many examples of relations whose entire sets of maximals and undominated maximals are completely identifiable in an elementary way. [ABSTRACT FROM AUTHOR]

In this paper, by using the Leggett–Williams fixed-point theorem, we study the existence of positive solutions to fractional differential equations with mixed Riemann–Liouville and quantum fractional derivatives. To prove the effectiveness of our main result, we investigate an interesting example. [ABSTRACT FROM AUTHOR]

The information about main results on geometry of developable surfaces with an edge of regression which have a directrix ellipse in the base is gathered. These surfaces constitute a group called “Ruled surfaces of conical type on elliptical base”. This group includes elliptical cones, torses with two ellipses defined in the parallel planes, equal slope surfaces, and ruled surfaces with the main frame of three superellipses that are ellipses in one coordinate plane and broken straight lines in the other two coordinate planes. The paper presents a method for developing torses onto a plane, approximation of torses by folded surfaces, and parabolic ending of a thin sheet from elastic material into a torse shell. A brief review of the methods of stress-strain and buckling analysis of the considered ruled shells is given, including the displacement-based finite element method and variational energy method. It is shown that analytical methods can be used only in the case of applying the momentless shell theory for ruled thin shells of conical type. The analytical formulae for determining the normal and tangent internal forces in any momentless conic shell with a superellipse in the base are derived. References to forty four scientific articles of other authors, working or having worked on the subject of the paper are given. These references confirm the conclusions of the author and the perspectives of investigations of the considered ruled surfaces and shells.

We present some sufficient conditions for the existence of positive solutions to a third order differential equation subject to nonlocal boundary conditions. Our approach is based on the Krasnosel'skiı-Guo fixed point theorem in cones and the properties of the Green's function corresponding to the BVP under study. The main results are illustrated by suitable examples. [ABSTRACT FROM AUTHOR]

The current study investigates to characterize the Complex Programming Problem (CPP) solution in a fuzzy environment. The paper is divided into two parts: 1) the first presents a Fuzzy Complex Programming Problem (FCPP) with fuzzy complex constraints, and 2) the second presents the optimality criteria using the fuzzy complex cone. The CPP is suggested by involving fuzzy numbers in the constraints in parts. Using the α -cut set concepts, the problem is converted into the α -complex programming. A number of basic theorems with proofs are established concerning the basic results for the fuzzy complex set of solutions for the F-CPP, and the optimality criteria of the saddle point for F-CPP with fuzzy cones is derived. [ABSTRACT FROM AUTHOR]

In this paper we consider a iterative system of two-point boundary value problems with integral boundary conditions having n singularities and involve an increasing homeomorphism, positive homomorphism operator. By applying Hölder's inequality and Krasnoselskii's cone fixed point theorem in a Banach space, we derive sufficient conditions for the existence of denumerably many positive solutions. Finally we provide an example to check validity of our obtained results. [ABSTRACT FROM AUTHOR]

The movement of microorganism cells in fluid influences various biotic processes, including septicity and marine life ecology. Many organic and medicinal applications need to look into the insight of mechanism in nanofluids containing a microbial suspension. The current paper concerns the bioconvection of a ternary hybrid nanofluid (Al2O3-Cu-CNT/water) flow containing motile gyrotactic microorganisms toward three different geometries (a flat plate, a wedge, and a cone) in the occurrence of natural convection, radiation, and heat source/sink. The Cattaneo–Christov theory is employed to develop the model. The equations are solved by using the "bvp4c function in MATLAB". The influence of the crucial significant factors on the motile microorganisms' density, velocity, temperature, nanoparticles' concentration, microbe density gradient, and transmission rates of heat and mass is discussed. The results depict that the heat transmission rate is highest for the flow toward the cone, whereas the mass transmission rate and microbe density gradient are highest for the flow toward the wedge. In addition, the higher estimates of the thermal relaxation parameter corresponding to the Cattaneo–Christov theory act to enhance the rate of heat transmission. The results of the current study will be useful to many microbial-enhanced oil recovery systems, carriage processes, architectural design systems, medicinal fields that utilize nanofluids, and so on. [ABSTRACT FROM AUTHOR]

In this paper, by using the Guo-Krasnoselskii theorem, we investigate the existence and nonexistence of positive solutions of a class of boundary value problem of third-order nonlinear differential equation involving Stieltjes integral conditions. Under some growth conditions imposed on the nonlinear term, we obtain explicit ranges of values of parameters with which the problem has a positive solution and has no positive solution respectively. An example is given to illustrate the main results of the paper. [ABSTRACT FROM AUTHOR]

The precise three-dimensional measurement of fuel nozzles is of great significance to assess the manufacturing accuracy and improve the spray and atomization performance. This paper proposes an improved fast shape from focus (SFF) method for three-dimensional measurement of key features of fuel nozzles. In order to ensure the measurement accuracy and efficiency of the SFF, the dispersion of the measured points from a standard flat plane was used to select the optimal combination of the focus measure operator, window size and sampling step size. In addition, an approximate method for the focus measure interval is proposed to improve the measurement efficiency, which uses the peak region of the central pixel to replace the peak region of other pixels. The results show that the proposed method decreased the average computation time of the focus measure by 79.19% for the cone section and by 38.30% for the swirl slot. Compared with a reference laser scanning microscope, the measurement error in length is within 10 μm and the error in angle is within a maximum 0.15°. [ABSTRACT FROM AUTHOR]

The electro-hydraulic plastic deforming method belongs to non-conventional plastic deforming techniques class. The shape of the discharging chamber and of the energy concentrators influences workpiece machining, along with the other parameters of the equipment (electrical pulses, electrodes, space between electrodes, pressure wave transmission medium, way to propagate the pressure wave). The paper proposes a comparative analysis of the geometric parameters of the discharging chambers and of their effects on the technological processing. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of positive solutions of the fully fourth-order boundary value pqroblem u (4) = f (t , u , u ′ , u ″ , u ‴) on [ 0 , 1 ] with the boundary condition u (0) = u (1) = u ″ (0) = u ″ (1) = 0 , which models a statically bending elastic beam whose two ends are simply supported, where f : [ 0 , 1 ] × R + × R × R − × R → R + is continuous. Some precise inequality conditions on f guaranteeing the existence of positive solutions are presented. The inequality conditions allow that f (t , u , v , w , z) may be asymptotically linear, superlinear, or sublinear on u , v , w , and z as | (u , v , w , z) | → 0 and | (u , v , w , z) | → ∞ . Our discussion is based on the fixed point index theory in cones. [ABSTRACT FROM AUTHOR]

Finding the position of a radiative source based on time-difference-of-arrival (TDOA) measurements from spatially separated receivers has been widely applied in sonar, radar, mobile communications and sensor networks. For the nonlinear model in the process of positioning, Taylor series and other novel methods are proposed. The idea of cone constraint provides a new way of solving this problem. However, these approaches do not always perform well and are away from the Cramer-Rao-Lower-Bound (CRLB) in the situations when the source is set at the array edge, the noise in measurement is loud, or the initial position is biased. This paper presents a weighted-least-squares (WLS) algorithm with the cone tangent plane constraint for hyperbolic positioning. The method adds the range between the source and the reference sensor as a dimension. So, the space-range frame is established. Different from other cone theories, this paper sets the reference sensor as the apex and finds the optimal source estimation on the cone. WLS is used for the optimal result from the measurement plane equations, a vertical constraint and a cone constraint. The cone constraint equation is linearized by a tangent plane. This method iterates through loops and updates the tangent plane, which approximates the truth-value on the cone. The proposed algorithm was simulated and verified under various conditions of different source positions and noises. Besides, some state-of-the-art algorithms were compared in these simulations. The results show that this algorithm is accurate and robust under poor external environment. [ABSTRACT FROM AUTHOR]

In this paper, we establish infinitely many positive solutions for the iterative system of conformable fractional order dynamic equations on time scales TαΔ[ TβΔ (Vn(t))] = φ(t) fn(Vn+1(t)), t ∈ (0, 1)핋, 1 < α, β ≤ 2 V1(t) = Vl+1 (t), t ∈ (0, 1)핋, n = 1, 2, ..., l, satisfying two-point Riemann--Stieltjes integral boundary conditions Vn(0) = 0, Vn(1) = ∫0¹ Vn(τ)g(τ), n = 1, 2, ..., l, (TβΔVn)(0) = 0, (TβΔVn) (1) = ∫0¹ (TβΔVn) (τ)g(τ), n = 1, 2, ..., l, where T*Δ denotes the conformable fractional derivative of order * ∈ {α, β} on time scale T, by an application of Krasnoselskii's fixed point theorem on a Banach space. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some results about the existence of multiple solutions for the following singular semipositone boundary value problem of fourth-order differential systems with parameters: { u (4) (t) + β 1 u ″ (t) − α 1 u (t) = f 1 (t , u (t) , v (t)) , 0 < t < 1 ; v (4) (t) + β 2 v ″ (t) − α 2 v (t) = f 2 (t , u (t) , v (t)) , 0 < t < 1 ; u (0) = u (1) = u ″ (0) = u ″ (1) = 0 ; v (0) = v (1) = v ″ (0) = v ″ (1) = 0 , where f 1 , f 2 ∈ C [ (0 , 1) × R 0 + × R , R ] , R 0 + = (0 , + ∞) . By constructing a special cone and applying fixed point index theory, some new existence results of multiple solutions for the considered system are obtained under some suitable assumptions. Finally, an example is worked out to illustrate the main results. [ABSTRACT FROM AUTHOR]

The focus of this paper revolves around the examination of flow of ternary hybrid nanofluid, specifically the Al2O3–Cu-CNT/water mixture, with buoyancy effect, across three distinct geometries: a wedge, a flat plate, and a cone. The study takes into account the presence of quadratic thermal radiation and heat source/sink of non-uniform nature. To develop the model, the Cattaneo–Christov theory is utilized. The equations governing the flow are solved by applying similarity transformations and employing the ''bvp4c function in MATLAB” for numerical analysis and solution. Conventional methods for conducting parametric studies often face challenges in producing significant conclusions owing to the inherent complex form of the model and the method involved. To address the aforementioned issue, this paper explores the potential of machine learning methods to foresee the conduct of the flow characterized by multiple interconnected parameters. By utilizing simulated data, an artificial neural network is trained using the Levenberg-Marquardt algorithm to learn and comprehend the underlying patterns. Subsequently, the trained neural network is employed to estimate the Nusselt number on the surfaces of all three geometries. This approach offers a promising alternative to traditional parametric studies, enabling more precise predictions and insights into the behavior of complex systems. The Nusselt number is highest for THNF flow over the cone. The mean squared error (MSE) values for the ANN algorithm, across all analyzed cases, range from 0 to 0.03972. The findings contribute to an improved understanding of the characteristics and dynamics of ternary hybrid nanofluid flow in various geometries, assisting in the design and optimization of heat transfer systems involving such fluids.

In this paper we present an extension of the original version of Leggett-Williams fixed point theorem for a k -set contraction perturbed by an expansive operator. Our approach is applied to prove the existence of non trivial positive solutions for initial value problems (IVPs for short) covering a class two-dimensional nonlinear wave equations. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence and multiplicity of positive solutions for a system of fractional differential equations with boundary condition and advanced arguments. The existence result is proved via Leray–Schauder's fixed point theorem type in a vector Banach space. Further, by using a new fixed point theorem in order Banach space, we study the multiplicity of positive solutions. Finally, some examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

In the paper we consider the boundary value problem of heat conduction outside the cone, i.e. in the domain degenerating into a point at the initial moment of time. In this case, the boundary condition contain a derivative with respect to the time variable. The peculiarity of the problem under consideration consists precisely in the presence of a moving boundary and the degeneration of the solution domain into a point at the initial moment of time. The well-known classical methods are generally not applicable to this type of problems. By the method of heat potentials, such boundary value problems of heat conduction are reduced to the solution of singular Volterra type integral equations of the second kind A singular Volterra type equation is understood as an equation whose kernel has the following property: the integral of the kernel of the equation does not tend to zero as the upper limit tends to the lower one. Such integral equations cannot be solved by the method of successive approximations, and in most cases the corresponding homogeneous integral equations have nonzero solutions. We prove a theorem on the solvability of the considered boundary value problem in weighted spaces of essentially bounded functions. The issues of solvability of the singular Volterra integral equation of the second kind, to which the original problem is reduced, are studied. We found a nonzero solution of this singular integral equation. [ABSTRACT FROM AUTHOR]

The paper presents: intersection between two cylinders - one is a rotation cylinder and the other is an oblique circular cylinder; intersection between a rotation cylinder with an oblique circular cone. This method can be applied if the axes of the two surfaces are coplanar. The paper also presents the equations of the intersection curves which become simpler when the two surfaces are rotation cylinders. In this case the auxiliary spheres center is fixed at the axis intersection of the two rotation cylinders. The auxiliary spheres method with mobile center can be applied when a rotation cylinder is intersected with a torus or an oblique cone. The method is often used because it is rapid and allows intersection curve drawing using only a projection of the two surfaces. [ABSTRACT FROM AUTHOR]

Suppose that M is a strictly convex and closed hypersurface in En+1 with the origin o in its interior. We consider the homogeneous function g of positive degree d satisfying M = g −1(1) . Then, for a positive number h the level hypersurface g −1(h) of g is a homothetic hypersurface of M with respect to the origin o. In this paper, for tangent hyperplanes Φh to g −1(h) (0 < h < 1), we study the (n + 1) -dimensional volume of the region enclosed by Φh and the hypersurface M, etc.. As a result, with the aid of the theorem of Blaschke and Deicke for proper affine hypersphere centered at the origin, we establish some characterizations for ellipsoids in En+1 . As a corollary, we extend Schneider’s characterization for ellipsoids in E3 . Finally, for further study, we raise a question for elliptic paraboloids which was originally conjectured by Golomb. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the positive solutions of beam equations with the nonlinearities including the slope and bending moment under nonlocal boundary conditions involving Stieltjes integrals. We pose some inequality conditions on nonlinearities and the spectral radius conditions on associated linear operators. These conditions mean that the nonlinearities have superlinear or sublinear growth. The existence of positive solutions is obtained by fixed point index on cones in C 2 [ 0 , 1 ] , and some examples are given for beam equations subject to mixed integral and multi-point boundary conditions with sign-changing coefficients. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of three positive periodic solutions for a class of second order neutral functional differential equations involving the delayed derivative term in nonlinearity (x (t) − c x (t − δ)) ″ + a (t) g (x (t)) x (t) = λ b (t) f (t , x (t) , x (t − τ 1 (t)) , x ′ (t − τ 2 (t))) . By utilizing the perturbation method of positive operator and Leggett–Williams fixed point theorem, a group of sufficient conditions are established. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiplicity results of some positive solutions for a system of Hadamard fractional differential equations with parameters and p-Laplacian operator subject to three-point boundary conditions which contains fractional derivatives. The proofs of our main result, multiplicity of positive solutions, are derived in terms of different values of parameters by using Guo–Krasnosel'skii's fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we propose extensions of Leray-Schauder boundary condition for a sum of two operators T + S in the case when T is an expansive operator and I − S is a completely continuous operator. As their applications, we investigate a class of fourth-order nonlinear boundary value problems with integral boundary conditions. We give conditions for the parameters of the considered boundary value problem that ensure existence of at least two non trivial bounded nonnegative classical solutions of the considered boundary value problem. The results in the paper are provided with a suitable example.

In this paper, by using a new type of Carleman formula with respect to a certain Laplace operator, we estimate the growth property for solutions of certain Laplace equations defined in a smooth cone. [ABSTRACT FROM AUTHOR]

In this paper, we not only give the asymptotic behavior at the origin for the maximum modulus of weak solutions of the stationary Schrödinger equation in a cone but also obtain the property of the negative parts of them, which generalize the Phragmén-Lindelöf type theorems for subfunctions. [ABSTRACT FROM AUTHOR]

This paper gives the growth property of certain harmonic functions at infinity in an n-dimensional cone, which generalize the results obtained by Huang and Qiao (Abstr. Appl. Anal. 2012:203096, ), Xu et al. (Bound. Value Probl. 2013:262, ), Yang and Ren (Proc. Indian Acad. Sci. Math. Sci. 124(2): 175-178, ) and Zhao and Yamada (J. Inequal. Appl. 2014:497, ) to the conical case. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence of positive solutions for a discrete third-order boundary value problems, which has the sign-changing Green's function. The approach we use is the Guo-Krasnoselskii fixed point theorem in a cone. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of nonlinear third-order boundary value problems with integral boundary conditions on time scales. By applying a generalization of the Leggett-Williams fixed point theorem, we establish the existence of at least three positive solutions. The discussed problem involves both an increasing and positive homomorphism, which generalizes the p-Laplacian operator. As an application, we give an example to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper we investigate a parameter-dependent nonlocal differential equations with convolution coefficients. Using the Birkhoff–Kellogg type theorem, existence of positive solutions is established. Under additional growth conditions, we obtain upper and lower bounds for the parameter. An example is also given to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, we will use the Krasnosel'skii fixed point theorem to investigate a discrete fractional boundary value problem of the form -Δvy(t) = λh(t+v-1)f(y(t+v-1)),y(v-2) =Ψ(y),y(v+b) =Φ(y), where 1N0,f: [0,∞)→[0,∞) is a continuous function, h: [v-1, v+b-1]Nv-1→[0,∞), Ψ,Φ: Rb+3→R are given functionals, where Ψ,Φ are linear functionals, and λ is a positive parameter. [ABSTRACT FROM AUTHOR]

A reverse experiment technique is used along with the technology of measuring rods to study the impact and penetration of a steel conical body in frozen sandy soil. This paper presents the dependences of maximum values of the force of resistance of cones with base diameters of 10.0, 12.0, and 19.8 mm to penetration into sand on the impact velocity in the range of values 100-400 m/s. The numerical solution of the problem in an axisymmetric formulation with the use of the “Dinamika-2” software package is used to show the effect of waves reflected from the walls of the container on the contact force. A comparative analysis of the forces of resistance to penetration of the shocker into compacted dry, water-saturated, and frozen sandy soils is carried out. [ABSTRACT FROM AUTHOR]

In this paper, we compute the Möbius function of pointed integer partition and pointed ordered set partition using topological and analytic methods. We show that the associated order complex is a wedge of spheres and compute the associated reduced homology group for each subposet. In addition, we compute the Möbius function of pointed graded lattice and use our method to compute the Möbius function of pointed direct sum decomposition of vector spaces. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to obtain a general theorem on existence of continuous branch of solutions of equations which depend on a parameter by using the monotone minorant method in conjunction with the theory of fixed point index. As an application, we apply this theorem to prove the existence of a positive eigen-pair of multivalued homogeneous increasing operators. The simplicity and uniqueness of the eigen-pair are also investigated in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of positive solutions to the boundary-value problem with fractional order (CaDαy)(t) +q(t)f(y) = 0, 0 ≤ a < t < b, 1 < α < 2, y(a) = 0, y(b) = βy(η), where a < η < b and β(η − a) − b + a ≠ 0. We prove the existence of at least one positive solution when f is either superlinear or sublinear using the well-known Guo-Lakshmikantham fixed point theorem in cones. Moreover, the convexity and concavity of the solutions are investigated with respect to the behavior of the function q. [ABSTRACT FROM AUTHOR]

This paper considers a class of fractional impulsive wave equations and improves a previous results. In fact, this paper adopts a new topological approach to prove the existence of classical solutions with a complex arguments caused by impulsive perturbations. To the best of our knowledge, there is a severe lack of results related to such impulsive equations.

In this paper, we consider nonlinear second order m-point impul- sive time scale boundary value problems on infinite intervals. We establish criteria for the existence of positive solutions to the nonlinear impulsive time scale boundary value problems on infinite intervals by using a result from the theory of fixed point index. [ABSTRACT FROM AUTHOR]

This paper discusses the natural convection boundary layer flow of a micropolar nanofluid over a vertical permeable cone with variable wall temperatures. Non-similar solutions are obtained. The nonlinearly coupled differential equations under the boundary layer approximations governing the flow are solved numerically using an efficient, iterative, tri-diagonal, implicit finite difference method. Different experimental correlations for both nanofluid effective viscosity and nanofluid thermal conductivity are considered. It is found that as the vortex-viscosity parameter increases, both the velocity profiles and the local Nusselt number decrease. Also, among all the nanoparticles considered in this investigation, Cu gives a good convection. [ABSTRACT FROM AUTHOR]