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Natural rheologic balancing is being state-of-the-art in developing polymer melt channels for extrusion dies or hot runners in injection molding. For this, flow path lengths and channel diameters in a manifold system are defined identical on all paths and thus those channels are considered to be identical in pressure drop and cavity filling, respectively in mass flow distribution. However, the changes in direction of the melt flow due to the deflection of the melt are in most cases neglected but have a significant impact on the flow field in downstream components. Strong deflections, as they occur in conventional manifold systems, can be avoided by the use of additive manufacturing methods. However, the bionic design leads to curved melt channels which, when naturally balanced, may differ completely from one another regarding their overall course and curvature. Therefore, unequal mass flow distributions or cavity fillings occur in such geometries. The aim of this paper is to investigate the influence of channel curvature on the balancing of additively manufactured melt channels. For this purpose, a test specimen is designed and the curvature collectives along the neutral fibers are evaluated. The overall objective is a more specific balancing with respect to the mass flow distribution. The results indicate the necessity of considering the channels' curvature in the designing process in order to achieve a homogeneous melt distribution. [ABSTRACT FROM AUTHOR]

Combining several results from the previous works of the author, three main subtleties will be clarified here. First, similar to the rotating BTZ black holes, we show how for the warped BTZ black holes, the consideration of the effective temperatures could solve the seemingly unsaturation issue of the chaos bound. Second, comparing the Hawking-Page phase diagrams of BTZ and warped BTZ black holes in the topologically massive gravity and new massive gravity theories, we show how the characteristics of the action would specify the behaviors of the chaos modes, and there we emphasize the importance of using the local and "physical" thermodynamical ensembles for studying the boundary chaos modes in warped CFTs and also the connections with the bulk reconstruction. Third, we propose that the boundary modular scrambling modes which saturate the modular chaos bound are related to the curvature invariants in the geometrical side. [ABSTRACT FROM AUTHOR]

The paper generalizes the concept of spherical mapping of a surface of Euclidean space. The R-curvature of a surface introduced by Ilya J. Bakelman and the extrinsic curvature of a surface in Galilean space introduced by A. Artykbaev are special cases of generalized extrinsic curvature. General and some special properties of the generalized extrinsic curvature are proved. The generalized extrinsic curvature is also a discrete function of a set and unlike spherical mapping of a surface can take any positive value and can be infinity. [ABSTRACT FROM AUTHOR]

This Research studied the(GC) Conharmonic curvature tensor of almost kahler-manifold, where this research focuses on the geometrical feature or properties of the one of the almost kahler-manifold. We arrived at the following results, Demonstrated that this tensor in this manifold has the conventional Riemannian curvature symmetry features. The eight non-zero components' values are determined. Some results have been obtained, as well as, the correlation between the eight non-zero components of W2 manifold's tensor has been established, Get a neutral equation for these components (GC)0, (GC)1, (GC)2, (GC)3, (GC)4, (GC)5, (GC)6, (GC)7, of almost kahler is haler manifold [ABSTRACT FROM AUTHOR]

In this paper we study the w-projective curvature tensor of nearly kahler manifold, i.e. The geometrical properties of one of the AH ("Almost Hermitian")-manifold structures are given by W1, where W1 indicates the almost Kahler manifold, and the w-Projective tensor of a nearly Kahler manifold has been examined in this research. The following are the important conclusions of the study:-The typical Riemannian curvature symmetry features of this tensor were demonstrated. In the NK-manifold, calculate the Projective tensor (W-tensor) components. Some observations were obtained, and links between the tensor components of this manifold were constructed. For these components w0, w1, w2, w3, w4, w5, w6, w7 of virtually kahler is haler manifold, provide a neutral equation. [ABSTRACT FROM AUTHOR]

In the current study, reinforced concrete ring deep beams that have different curvatures were studied. The finite element technique was utilized to analyze sixteen specimens. The parameters of the current investigation are beam height, width, compressive strength of concrete, and loading type. It was found that increasing the beam height by about 48-193% increases the moment of inertia, which raises the load capacity by about 59-218% and reduces the midspan deflection by about 22-41%. When increasing beam width by about 50-163%, the beam cross-section area increases, which rises the loading capacity by about 69-246% and reduces midspan deflection by about 7.8-22.8%. In addition to that, increasing strength of concrete by 12-47%, increases the failure load and midspan deflection by 11-36% and 5-12%, respectively. Finally, applying uniformly distributed load instead of midspan concentrated one, stresses are more distributed along the whole beam length leading to midspan deflection decrease by about 2.3-24% and loading capacity increase by 4.5-47%. [ABSTRACT FROM AUTHOR]

This study aims to investigate adequacy of the RILEM residual stress modelling approach. For this, the residual stress strain relations composed using the tests results of standard notched beam are compared to the stress - strain diagrams inversely obtained from the experimental moment-curvature response of RC beams reinforced with steel fibers. For this purpose, an experimental study of 8 full-scale SFRC beams with longitudinal reinforcement bars including the tests of standard notched beams was carried out. The varying parameters were volume levels of fibres and reinforcement ratio. To produce accurate moment – curvature diagrams, the beams were tested in four-point bending with measured strains at four levels throughout the constant bending zone. The predicted curvatures of SFRC beams following the RILEM recommendations were compared to the tests. Similarly, the residual stress - strain relations inversely derived from the structural tests were compared to the RILEM model. [ABSTRACT FROM AUTHOR]

This study proposes a Mach-Zehnder interferometer (MZI) based on double cladding fiber (DCF) for high curvature measurement. In this proposed design, two optical paths are paved in the core and in the inner cladding of the DCF. The outer cladding of DCF provides confinement of light in the inner cladding, hence enabling higher curvature to be imposed without any significant optical loss. The experiment revealed that the sensor exhibited the highest sensitivity values at 1.3484 nm/m−1 and −0.1367 nm/m−1 for low and high curvature ranging from 0.0 to 3.32 m−1 and from 62.5 to 142.8 m−1, respectively. To the best of the author's knowledge, this has been the largest curvature range measured by a fiber interferometer sensor. With such capability, the proposed sensor displays exceptional potential to be deployed in applications that involve high curvature measurement, such as in soft robotic, wearable medical device, and structural health monitoring system. [ABSTRACT FROM AUTHOR]

Asymmetric laminates could exhibit unique behaviour of bistable response. This allows them to be attractive for applications that require a large deflection with a relatively small input energy. This work focuses on the measurement of the deflection profile of multidirectional carbon/epoxy composites. Four stacking sequences were considered: [0/90], [0/45], [45/0/90] and [45/–45/0/90]. The specimens were scanned using a three-dimensional laser scanner. The deflection data was then extracted at 25 equally spaced locations on the specimens. Next, the location and the magnitude of the maximum and minimum deflection were identified and compared. The findings from this paper provides some preliminary information on the curvature of the multidirectional composite laminates with the effect of number of plies and fibre orientation of the adjacent layers. [ABSTRACT FROM AUTHOR]

Let M be a compact manifold. Let W be a smooth Hilbert A-module bundle over M equipped with connection and curvature, where A is an unital C∗-algebra. After reviewing some literature, we are inspired that an analog of the odd Chern character form can be defined in the Hilbert A-module bundle setting. In this paper, an explicit description of the odd Chern character form on W is provided via Getzler's method through the Chern-Simons form. Then, the properties of the Chern-Simons form and the odd Chern character are provided under this setting. Lastly, a commutative diagram involving the K-theory with coefficients in C∗-algebra, K0(M × 풮1; A) and K1(M; A) is established and related to its associated cohomology group respectively. [ABSTRACT FROM AUTHOR]

The paper treats conformal mappings of pseudo-Riemannian manifolds preserving the curvature of two-dimensional platforms. It is demonstrated that in the case of metrics with positive sign, this property relates only to the spaces of constant curvature. In the case of metrics with indefinite sign, the latter are joined by subprojective spaces of Kagan. [ABSTRACT FROM AUTHOR]

In 1967, Chen and Takashi deliberate some results of hypersurfaces properties on Kaehlerian manifolds. After that, in 2010, Negi and Semwal premeditated on Einstein-Kaehlerian Manifold with Recurrent Projective Curvature Tensor properties. Again, Negi (2016) willful study some Recurrence Properties in Kaehlerian, Einstein-Kaehlerian and Tachibana Spaces. The purpose of this paper, we calculated the invariable holomorphic curvature fascinated in Einstein-Kaehler manifolds and its related theorems established. [ABSTRACT FROM AUTHOR]

The drawing method of diagrams "bending moment – curvature" that describe the cross-section stress-strain state of the reinforced concrete elements with consideration of an axial force is proposed in the article. Diagrams "bending moment – curvature" at different values of an axial force are shown. It is seen from the diagrams that compressive axial force increases the crack resistance of the cross-section but leads to the brittle destruction. The maximum bearing capacity of the cross-section is reached with application of the reduced axial force αN=0,4. Results of the reinforced concrete frame analysis with the usage of diagrams "bending moment – curvature" drawn with and without consideration of axial forces are compared with the results of the experimental research. Mistake does not exceed 1-2%. [ABSTRACT FROM AUTHOR]

We present a covariant definition of "scale" in the context of Ruppeiner Geometry. By means of examples, we illustrate how the choice of a scale affects the scalar curvature of Ruppeiner metrics. Taking into account Ruppeiner's Interaction Hypothesis, this suggests that the nature of microscopic interactions within a system might depend on the ensamble in which the system interacts with its surroundings. Thereby, we extend previous well-known results regarding the nonequivalence of ensembles in this approach to fluctuation theory. [ABSTRACT FROM AUTHOR]

Spine curvature disorders are scoliosis, lordosis, and kyphosis. These disorders are mainly caused by the bad habits of the person during sitting, standing, and lying. There are about 3 to 5 out of 1,000 people who are affected by spine curvature disorder. The current conventional method used for diagnose this disorder, such as radiography, goniometry and palpation. However, these conventional methods require human skills and can be time-consuming, resulting to exhaustion of logistic. Therefore, there is a need to solve this problem by creating a Graphical User Interface (GUI) to analyse the human body posture through the 3D reconstructed model of the person. Hence, 3D map meshing reconstruction of the human body method is proposed. This project divided into three parts, which are the development of the GUI for human posture analysis, clinical validation and posture analysis of the 3D model. The 3D model reconstructed from 3D mapping parameters shows 100% accuracy of the assessed point. The lowest difference of angle for the comparison between clinical method (goniometer) and the GUI for male is (A.Pe) 0.930±0.870 and 1.240±0.860 for female (P.Pe). This finding of 3D model assessment system can be helpful for medical doctor to diagnose patient who have spine problem. [ABSTRACT FROM AUTHOR]

Having analyzed the known technical means of surface tillage, we have found that most of them have a disadvantage - unsatisfactory quality of tillage, as well as a significant amount of soil clods larger than 50 mm on the surface of the field. The state of the issue and its analysis showed that the existing tillage methods of the surface of the field before sowing are implemented by various agricultural machines, which are equipped with working bodies in the form of rotating spherical discs. However, the problem of high-quality soil cultivation by such working bodies, which meets the quality criteria, remains unresolved. Therefore, there is a necessity to substantiate theoretically the optimal design parameters of spherical discs, their diameter and radius of curvature. For the developed combined tillage unit capable of working the soil to a depth of 0.12 meters. The optimal diameter of a spherical disc is 0.45 m and radius of a sphere (curvature) of a disc is 0.557 m. The use of a combined tillage unit improves the quality of soil cultivation, improves the water regime and air condition for the subsequent development of cultivated plants. In addition, several technological operations are carried out in one pass of the tillage unit, which gives an opportunity to reduce the loss of soil moisture. [ABSTRACT FROM AUTHOR]

For an efficient simulation of droplets in their most common spherical shape a spherical-symmetric 1D DSMC-based Vlasov-Enskog solver has been implemented in the PIC-DSMC framework PICLas. So far, primarily planar 1D simulations have been performed and discussed in literature, neglecting the surface curvature and the resulting increased pressure inside the droplet. This has a significant impact on the droplets, especially for sizes in the 10-nanometer range, as this work shows from the results of the evaporation coefficients. [ABSTRACT FROM AUTHOR]

This research investigated the behavior of hollow normal and lightweight reinforced concrete arch beams. The experimental program consists of (8) simply supported arch beams specimens testing under a four-points load. For all specimens, the width (b) was 150 mm variable depth of 100-150 mm at mid-span, 1500 mm was the total length, 1400 mm was the effective span, and 466 mm was the shear span. It includes four groups (G1, G2, G3, and G4) to study the following parameter: curvature degree, replacement ratios of lightweight coarse aggregate (partially replacement of normal coarse aggregate by thermostone with different percentages of 50% and 75%, respectively), voids ratio, ultimate load, cracking load and strain distribution. Specimens were studied for comparisons between all beams (for hollow and solid beams). The result indicates that the curvature degree and voids ratio reduced the ultimate load while increases the maximum deflection of the normal reinforced concrete arch beam. For a replacement ratio of 50% normal coarse aggregate by thermostone for hollow beams with different curvature degrees, the ultimate load and maximum deflection decreases by about (9.9%-37.5%) and (14.24%-27.2%) respectively, compared with normal hollow concrete. While the replacement ratio of 75% normal coarse aggregate by thermostone for hollow beams with different curvature degrees, the ultimate load and maximum deflection decreased by about (42.86%-46.79%) and (16.26%-31.71%) respectively, compared with normal hollow concrete. [ABSTRACT FROM AUTHOR]

This paper displays the horizontal curvature (circular curvature) effect on deep beams using finite element analysis. Thirty-five reinforced concretes horizontally arched deep beams were analyzed. The parameters that were taken into consideration in the current work are the curvature angle (α) and beam height (H) while keeping one constant value for the beam length (L), i.e., different length to depth ratios (L/H). It is found that for L/H=2; the load capacity decreases by about 38-73% and 16-67%, respectively, when changing α from ∞ (straight beam) to 180 degrees, while torsional moments increase by about 74-174%. Negative bending moments decrease by about 13-56% when changing α from 30 to 180 degrees. The deflection decreases by about 0.1-1.8% when changing α from ∞ to 90 degrees. For L/H=2.5; The load capacity decreases by about 36-73% and 15-67%, respectively, when changing α from ∞ to 180 degrees, while torsional moments increase by about 73-168%. Negative bending moments decrease by about 14-57% when increasing α from 30 to 180 degrees. Decreasing deflection by about 4.1-5.9% when increasing α from 60 to 90 degrees. For L/H=3; load capacity decreases by about 34-73% and 14-68%, respectively, when changing α from 0 to 180 degrees, while torsional moments increase by about 71-161%. Negative bending moments decrease by about 15-58% when increasing α from 30 to 180 degrees. The deflection decreases by about 6-9.7% when increasing curvature angle from 60 to 90 degrees. For L/H=3.5; the load capacity decreases by about 34-73% and 14-69%, respectively, when changing α from 0 to 180 degrees, while torsional moments increase by about 70-156%. Negative bending moments decrease by about 15-59% when changing α from 30 to 180 degrees. Midspan deflection decreases by about 4.6-14.7% when changing α from 60 to 120 degrees. Finally, it is found that for L/H=4; The load capacity decreases by about 33-74% and 14-69%, respectively, when changing α from 0 to 180 degrees, while torsional moments increase by about 69-150%. Negative bending moments decrease by about 16-60% when changing α from 30 to 180 degrees. Changing α from 60 to 120 degrees leads to decrease deflection by about 9.1-19.4%. [ABSTRACT FROM AUTHOR]

The detection of damage in the beam structure is an essential factor of the decision-making process concerning their repair and a complete replacement. For this purpose, an upgraded technique based on the finite element approach is used in this paper for the identification of the extent of the damage for a simply supported steel beam via the frequency response function curvature (FRFC) and its position. The harm is simulated by reducing the rigidity of selected elements at a constant viscous damping ratio for different locations with 30% reduction in stiffness. The MATLAB software is modeled on three cases of damage, unity, two, and three damage locations. Based on the results, the best way to show FRFC's value is by using the Root Mean square in both the first and third modes. The damage detection is represented by a peak in the response curve. This method can be analyzed and evaluated the beam structures and the damage by using the modifications occurred in its dynamic characteristics. The results of the study showed that the normalized curvature approach for frequency response works well for the identification damage as 100%. [ABSTRACT FROM AUTHOR]

Medical image processing requires image segmentation and image registration as important diagnostic tools. Image segmentation aims to split structures of interest into distinct components. Meanwhile, image registration finds an ideal transformation between given images. Despite their interrelationship, both tasks are often performed separately. As a result, it faces several problems when undertaken independently. Therefore, the joint models between segmentation and registration have advantages over the separate tasks, particularly when dealing with noisy images. This paper reviewed and compared three existing variational joint segmentation and registration (JSR) models based on active contour without edges and linear curvature. The models are tested on 2D mono-modal and multi-modal images with the presence of white Gaussian noise. The Dice coefficient metric and the registration performance measure are used to evaluate the performance of the models. Numerical results showed that the JSR model using the modified sum of the squared difference outperformed the other two JSR models for noisy mono-modal images. However, the JSR model using the modified normalized gradient fields performed better than the JSR model based on the modified mutual information for noisy multi-modal images. [ABSTRACT FROM AUTHOR]

Currently, no cost-effective and sustainable substitutes were developed for gel dosimeters. However, the properties of saluyot (Corchorus olitorius) may be integrated to improve the dose-response of the gel matrix. The study aimed to make a gel dosimeter using saluyot leaves. Specifically, this study aimed to describe the physical characteristics and assess the radiation detection capability of the fabricated saluyot gel dosimeter and to generate a dose-response curve using the ROI and R2 values. Saluyot leaves were sun-dried for 24 hours and powdered. The gel formulation consisted of gelatin (250 Bloom, Porcine) and finely powdered saluyot leaves which varied in the range of 4-9%, resulting in a mixture of 13% with 87% water for the final formulation. The gels were irradiated using a 6 MV photon beam by a LINAC. MRI was used as the imaging technique to scan for the dose distribution of the irradiated gel dosimeter. The images were subjected to post-analysis after scanning. The physical qualities of each dosimeter changed after irradiation, but the measured absorbed doses were in the range of the established limits. Based on the dose-response curvature and linearity, the 4% to 7% concentrations were the optimal range for an organic gel dosimeter. Lastly, this study showed that the ROI and stability were inversely related to the concentrations of powdered saluyot leaves. [ABSTRACT FROM AUTHOR]

The paper treats spaces that retain a curvature of three-dimensional platforms in the course of conformal mapping. Authors found a necessary condition for permitting of concircular vector fields by these spaces. It is proved that under these conditions the above-mentioned spaces are quasi-Einstein spaces of a special kind. [ABSTRACT FROM AUTHOR]

In this paper we study generalized ϕ-recurrent almost C(λ) manifolds. It is proved that a generalized ϕ-recurrent almost C(λ) manifold is an Einstein manifold. Wealso find some relations between the associated 1-forms. Also it is shown that generalized concircular, conformal ϕ-recurrent almost C(λ) Manifolds are Einsteins. Further it is proved that conservative concircular almost C(λ) manifold is an Einstein manifold and shown that the concircular curvature tensor is irrotational on almost C(λ) manifolds. [ABSTRACT FROM AUTHOR]

In this paper we study locally W1 and W8 curvature tensor of φ-symmetric K-contact manifolds w.r.t. the quarter-symmetric metric connection (briefly q-s-m connection) and some results are obtained. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to discuss the geometrical properties of a locally conformal almost cosymplectic manifold of constant curvature. In particular, the necessary and sufficient conditions for the aforementioned manifold to be of constant curvature have been determined. [ABSTRACT FROM AUTHOR]

In this work we propose a second-order accurate scheme for shallow water equations in general covariant coordinates over manifolds. In particular, the covariant parametrization in general covariant coordinates is induced by the metric tensor associ-ated to the manifold. The model is then re-written in a hyperbolic form with a tuple of conserved variables composed both of the evolving physical quantities and the metric coefficients. This formulation allows the numerical scheme to i) automatically compute the curvature of the manifold as long as the physical variables are evolved and ii) numerically study complex physical domains over simple computational domains. [ABSTRACT FROM AUTHOR]

This article proves that on a manifold with zero sectional curvature, if the submersion is Riemannian, then the foliation is a completely geodesic Riemannian foliation with isometric fibers. In addition, it is shown that if each component of the critical level surface is either a point or a regular surface, and they are isolated from each other, then the level surfaces of the function are conformally equivalent. [ABSTRACT FROM AUTHOR]

The paper presents experimental results on the verification of the reliability of one of the basic laws of the theory of plasticity - A. A. Ilyushin's isotropy postulate with complex elastoplastic deformation along trajectories of constant curvature in the form of semicircles. Experimental studies were carried out on thin-walled tubular specimens made of steel 45 on an automated testing machine SN-EVM. Loading programs for tubular specimens were set in the deviatorial strain space of A.A. Ilyushin (rigid or kinematic loading) with simultaneous combined action of tension-compression and torsion on the sample. A series of four experiments is considered, in which strain trajectories are realized, which are semicircles with a curvature of 133.3, starting from the origin. It is found that for the realized complex trajectories of constant curvature the isotropy postulate is fulfilled both in scalar and vector properties. [ABSTRACT FROM AUTHOR]

Path planning plays a major role in autonomous navigation. Different curve fitting methods are used in creating path for autonomous vehicles. Among those Bezier curves are widely used to create path especially in roundabouts due to their special properties. The primary factor that affects the shape and curvature of the Bezier curve is the control points. Researchers have established equations for calculating the control points for a Bezier curve travelling through selected points. The two critical elements that determine the control points are the random points selected for control point calculation and the segmentation factor (t) for each of the points selected. The values of segmentation factor (t) is assigned randomly to each point. As the segmentation factor change new control points are calculated which makes a change in the shape of the curve but the curve will pass through the selected points. So, this paper presents the change in the shape of the curve as the segmentation factor (t) changes. Additionally, it demonstrates the change in segmentation factor (t) for each point selected to fit the curve within the required space and to adjust t value for connecting two different Bezier curves to create a single curve with continuous curvature. This paper also presents an equation for finding the t value for each of the points selected to avoid overfitting and underfitting of the curve. [ABSTRACT FROM AUTHOR]

It is generally believed that the radiation of relativistic particles in a curved magnetic field proceeds in either the synchrotron or the curvature radiation modes. We study an intermediate, the so-called synchro-curvature regime. Using the Hamiltonian formalism, we find the trajectory of relativistic particle in the curved magnetic field that has the form of a helix wound around the drift trajectory. We show that the transition to the limit of the synchrotron and curvature radiation regimes is determined by relation between curvatures of the drift trajectory and gyration motion around it. When both are approximately equal, the curvature of the trajectory start to noticeably oscillate with the frequency of particle gyration leading to the synchro-curvature radiation with averaged spectrum different from synchrotron or curvature one. The performed numerical calculations with energy losses and different initial pitch angles confirm the principal conclusions based on the simplified analytical treatment. [ABSTRACT FROM AUTHOR]

In this paper we study, Projective and pseudo-Projective curvature tensors in Kenmotsu manifolds with respect to semi-symmetric connection. And obtained the results on ϕ -Projectvely and ϕ -pseudo-Projectvely flat Kenmotsu manifolds with semi-symmetric metric connection, [ABSTRACT FROM AUTHOR]

In this paper we study a special type of pseudo-Riemannian spaces quasi-Einstein spaces of constant scalar curvature. These spaces are generalizations of known Einstein spaces. We obtained a linear form of the basic equations of the theory of geodetic mappings for these spaces. The studies are conducted locally in tensor form, without restrictions on the sign and signature of the metric tensor. [ABSTRACT FROM AUTHOR]

The Hyperbolic MBO (HMBO) algorithm has been modified to handle the problem of obstacle. In this paper, we use this algorithm to simulate the movement of interface regarding the curvature dependent acceleration. The initial curves and the obstacle are considered as closed curves. An obstacle is placed within the initial curve. We examine the curve movement. In the obstacle problem, we obtain that the curve movement does not exceed the obstacle. After touching the obstacle, the curve attaches to it. [ABSTRACT FROM AUTHOR]

The article presents experimental data on the formation of film cooling on the suctions and pressure sides of a turbine blade near its leading edge under conditions of flow acceleration and wall curvature using V-shaped grooves behind the injection holes. It is shown that to achieve acceptable values of the efficiency of film cooling when using V-shaped grooves on the wall, a lower relative flow rate of the cooler can be used. The results can be used in the design of effective cooling systems for turbine blades. [ABSTRACT FROM AUTHOR]

In the present paper, we determine the holomorphic curvature tensor of generalized complex space forms and study some properties of this tensor in generalized complex space forms. Moreover, we present results on generalized complex space forms satisfying curvature identities named Walker type identities. [ABSTRACT FROM AUTHOR]

For the Riemannian space Vn, the invariantly associated with Vn space v̅²n is constructed, which implements a second order approximation for Vn. We studied conformal transformations when the original space is a space of non-zero constant curvature. [ABSTRACT FROM AUTHOR]

Arboriculture is one of the risk jobs in agriculture to make that easy to farmers many scientists have invented different kinds of tree climbing robot. Mostly treebot have difficulties in gripping the tree bark because of different in diameter and being flexible around the branches and curvature. It is challenging task to grab the rough and irregular surface of the tree. To overcome that, here in this study proposes the bionic koala treebot using Arduino, which have high gripping capacity around the different diameter and curvature of variety of tree. The algorithm of the treebot inspired by the tree climbing style of koala, the quadruped arms are construed with a smaller number of sensing source and limit switch without reprogramming for tree to tree. [ABSTRACT FROM AUTHOR]

The geometry of orbits of families of smooth vector fields is an important object of mathematics due to its importance in applications, in the theory of dynamic systems and in the foliation theory. The paper devoted to the applications of the geometry of orbits of vector fields in four dimensional Euclidean space in theory of differential equations. It is shown that orbits generate singular foliation ever regular leaf of which is a surface of negative Gauss curvature and zero normal torsion. In addition, the invariant functions of the considered vector fields are used to find solutions of the two-dimensional heat equation that are invariant under the groups of transformations generated by these vector fields. In this paper smoothness is smoothness of the class C∞. [ABSTRACT FROM AUTHOR]

The modified Einstein's field equations, that is the Einstein-Gauss-Bonnet, explain a higher dimensional curvature gravity which is expressed in terms of the Lanczos tensor and love lock. In this paper, we will find the constraint to solve the Einstein-Gauss-Bonnet, and use the constraint to obtain the differential equation and generate the solution generating theorems that apply to perfect fluid spheres. Finally, we analyze the result of the theorems and determine how to classify the metrics using these theorems. [ABSTRACT FROM AUTHOR]

The paper proposes a unique approach to designing the plan and profile of a hump yard. For the formation of the subgrade in the cross-section, it is proposed to use one-petal and two-petal hyperbolic paraboloids (hypars), and also, it is proposed a form of a hypersurface of a hump yard, in which the guide is a curve with negative Gaussian curvature, and the formative is a parabola (a curve with positive curvature). In order to ensure rapid rolling of cars and carriages on the surface of the hump it is proposed to replace the parabola with the apex in the hyperbolic paraboloid with the apex at the bottom, with a brachistochrone. As a result, to design the surface of the marshalling hump we get a shell of negative Gaussian curvature. [ABSTRACT FROM AUTHOR]

The tensor R · C − C · R and the tensors Q(g, R), Q(S, R), Q(g, C) and Q(S, C) of every Einstein manifold (M, g), n ≥ 4, satisfy R · C − C · R = (κ/((n − 1)n)) Q(g, R) = (κ/((n − 1)n)) Q(g, C) = (1/(n − 1)) Q(S, R) = (1/(n − 1)) Q(S, C). Motivated by this we study curvature properties of non-Einstein and non-conformally flat semi-Riemannian manifolds of dimension ≥ 4 satisfying the following family of generalized Einstein metric conditions: the tensor R · C − C · R is a linear combination of the tensors Q(g, R), Q(S, R), Q(g, C), Q(S, C), Q(g, g ∧ S) and Q(S, g ∧ S). We present results on quasi-Einstein and 2-quasi-Einstein warped product manifolds satisfying particular conditions of these family of conditions. [ABSTRACT FROM AUTHOR]

Kinematic bending processes such as three-roll-push-bending are used to manufacture freeform bent part systems. Due to the kinematic shaping, the bent parts have a characteristic infeed and outfeed area in the transition zone from the straight section into the curved area. These transition zones are currently not considered in the design process, which results in a geometric shape deviation between the CAD model and the bent part. Within this publication, a sensitivity analysis examines the influence of different parameters on the transition zone and the shape deviation. In addition, an approach is presented, which allows a manufacture-oriented modeling of the bending geometry. [ABSTRACT FROM AUTHOR]

Due to engineering application and its intricacy, flow in a curved duct has become one of the most challenging research fields of fluid mechanics. In this paper, a computational numerical study is presented for the flow through a curved rectangular duct of aspect ratio 4 with strong curvature δ = 0.5 for the pressure gradient, the Dean number, 100 ≤ Dn ≤1000. A spectral method is employed as the basic tool to solve the system of nonlinear partial differential equations while function expansion and collocation method as the secondary tools. First, solution structure of the steady solutions is investigated. As a result, three branches of symmetric/asymmetric steady solutions with multi-vortex solutions are obtained by the path continuation technique. Then, in order to investigate non-linear behavior of the unsteady solutions, time evolution calculations as well as their phase portraits are obtained, and it is found that typical transition occurs from a steady flow to a chaotic state through periodic or multi-periodic flows if Dn is increased no matter what the curvature is. Finally, distribution of the time dependent solutions is shown in the Dean number vs. curvature (Dn ∓ δ) plane with vortex structure of secondary flows. [ABSTRACT FROM AUTHOR]

Due to the application of thinner sheet steels, the stamped panels in the forming process, generally, are severely distorted. The wavy shape of embossed panel finally converted to residual stress embedded in the panel at final forming (edge L-bending) and it is known as the cause of twisting and oil canning of spring backed panel. Another important source of stamped shape deviation is the curvature of blank. The effects of blank curvature on the shape defects (panel curvature and twisting) after stamping were investigated from defective panel analysis, model experiment and stamping simulation. And the effect of tool conditions (BHF and bead height change) on spring backed shape of real TV bottom chassis were studied. The initial curvature of blank was remained in the flat area of stamped panels as width directional curvature. It converted from length direction curvature of blank. The curvature of initial blank reduced the wavy shape after local emboss forming, but twisting after edge L-bending was increased at large blank curvature cases. The effects of emboss forming conditions, the forming heights and blank holding force were studied and it was found that the wavy shape of stamped sheet was rapidly changed although the forming conditions altered very small amount. [ABSTRACT FROM AUTHOR]

It is shown that strain-induced defects of all kinds are nucleated in local curvature zones of the interfaces between 3D-crystals and 2D-planar subsystem similar to a laser pumping mechanism. Mobile curvature solitons are generalized wave structural carriers of plastic flow. Fracture is the structural phase decay of a crystal in the zones of very high curvature. [ABSTRACT FROM AUTHOR]

The paper treats pseudo-Riemannian spaces with the Riemann tensor of a particular structure. Riemann tensor's structure is defined by combinations of special symmetric and skew symmetric tensors. It is proved for every type of these spaces that the latter commute with Ricci tensor. The research is carried out in tensor form, without any limitations on a sign of a metric. [ABSTRACT FROM AUTHOR]

The disparity between the reaction and the engineering length scales in high-explosive (HE) systems motivates the use of programmed burn methods where the detonation wave is replaced with a surface and an evolution equation. When the normal detonation velocity differs from the nominal Chapman–Jouguet value (non-zero curvature), the local expansion isentrope of the HE detonation products must be mathematically consistent with the post-flow state to yield the correct detonation energy. The hydrodynamic step associated with the HE energy release is typically treated using a velocity-adjusted equation of state or a pseudo-reaction zone model. This paper describes a model where the bulk of the chemical energy is released instantaneously at the shock and the remainder is released at the finite rate dictated by a base reactive burn model. The implementation steps rely on existing code infrastructure and use the same parameter calibration as the base burn model. Two one-dimensional test cases are presented for a spherically diverging and a spherically converging detonation. The results show that the proposed methodology is able to capture the main flow features at coarse resolutions while retaining a strong hydrodynamic coupling. [ABSTRACT FROM AUTHOR]

In article the design procedure of the bending moment and curvature in a plastic zone of elastic-plastic calculation of the framework of the cabin of the tractor is offered. The offered method procedure of the bending moment and curvature in a plastic zone together with the known methods of calculation of an elastic zone allow with count deformation of the design of the framework with an accuracy, sufficient for the framework of cabins of the tractor. [ABSTRACT FROM AUTHOR]