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We introduce generalized Darboux frames along a null Cartan curve lying on a timelike surface in Minkowski space 피13 and define null Cartan normal isophotic and normal silhouette curves in terms of the vector field that lies in the normal plane of the curve and belongs to its generalized Darboux frame of the first kind. We investigate null Cartan normal isophotic and normal silhouette curves with constant geodesic curvature kg$$ {k}_g $$ and constant geodesic torsion τg$$ {\tau}_g $$. We obtain the parameter equations of their axes and prove that such curves are the null Cartan helices or the null Cartan cubics. In particular, we show that null Cartan normal isophotic curves with a non‐zero constant curvatures kg$$ {k}_g $$ and τg$$ {\tau}_g $$ have a remarkable property that they are general helices, relatively normal‐slant helices and isophotic curves with respect to the same axis. We prove that null Cartan cubics lying on a timelike surface are normal isophotic curves with a spacelike axis and normal silhouette curves with a lightlike axis. We obtain the relation between Minkowski Pythagorean hodograph cubic curves and null Cartan normal isophotic and normal silhouette curves. Finally, we give numerical examples of null Cartan normal isophotic and normal silhouette curves obtained by integrating the system of two the first order differential equations under the initial conditions. [ABSTRACT FROM AUTHOR]

In this paper, wavelet transform on a generalized helix space curves are investigated, including of local continuous wavelet transform at some point and discrete wavelet transform on a class of helix curves. Firstly, a class of helix space curves are introduced and the parameter equations are given. Then the dilation operator and translation on the function ψ (ξ 0) is properly defined by the local projection at some point from a space curve on the unit sphere onto its tangent line. The local continuous wavelet transform and its reconstruction formula are deduced at some point of a space curve on the unit sphere. On the other hand, According to the discretization of length-preserving projection, discrete wavelet transform is lifted onto a helix space curve, such as a circular helix curve. Based on length-preserving projection, the some properties are discussed, such as two-scale sequences of scaling function and wavelet, orthogonality, decomposition formula and so on. Finally, two examples are given for our discussion. One example is illustrating the application of local continuous wavelet transform at some point of a space curve. The result shows the signal at some point of a space curve can be reconstructed by local continuous wavelet method. The norm of the error is 0.3783 between original signal and reconstructed signal in this example. The other numerical example is given for decomposing and reconstructing with the signal on a circular helix curve. The result shows the signal on a helix space curve can be decomposed and reconstructed by the length-preserving projection. The norm of the error is 8.0741 × 10−11 between original signal and reconstructed signal. The figures are shown for the simulation results. [ABSTRACT FROM AUTHOR]

The involute of a curve is often called the perpendicular trajectories of the tangent vectors of a unit speed curve. Furthermore, the B-Lift curve is the curve acquired by combining the endpoints of the binormal vectors of a unit speed curve. In this study, we investigate the correspondences between the Frenet vectors of a curve's B-lift curve and its involute. We also give an illustration of a helix that resembles space in Lorentzian 3-space and show how to visualize these curves by deriving the B-Lift curve and its involute. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an alternative approach centered around an alternative moving frame for finding the position vector of a general helix given its curvature and torsion. Our methodology begins by formulating a vector differential equation, leveraging the unit principal normal vector of a general helix with the assistance of the alternative moving frame. Then, by solving this differential equation, we obtain the position vector of the general helix. This innovative technique is then applied to ascertain the position vector of a circular helix. To illustrate the effectiveness of our method, we showcase parametric representations of various general helices, each defined by unique curvature and torsion functions. [ABSTRACT FROM AUTHOR]

We give a method for constructing generalized null Cartan helices, which may have singularities, by using regular space-like plane curves and smooth functions in Minkowski 3-space. We also study the principle normal worldsheet, which is deeply related to generalized null Cartan helices from the viewpoint of singularity theory. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of curve called the k-directional Darboux curve. These curves are generated by vector fields that are constructed using the Darboux frame of a given spacelike curve α lying on a timelike surface in Minkowski 3-space E³1 We give the relationships between these curves and their curvatures. In particular, we show how k-directional Darboux curves can be used to classify some special curves, such as helices and slant helices. [ABSTRACT FROM AUTHOR]

The purpose of this study is to develop an evaluation method for assessing the relative relationship between gear tooth shape deviations on every gear tooth using network theory. Our previous study introduced a method for representing the phase difference between each helix deviation as a network, demonstrating that it is possible to identify the relative relationship between gear tooth deviations. However, there has been no in-depth analysis of the impact of injection molding on the gear's phase difference network. In this paper, we begin by measuring the gear tooth shape deviation, calculating the correlation coefficient, and expressing it as an adjacency matrix. When the adjacency matrix was visualized and displayed as a pixel plot, a periodic pattern was formed. The relationship between the position of the gate used to inject molten resin material into the injection mold and the pixel plot were then investigated in detail, and it was confirmed that the helix deviation network of a gear manufactured with the injection molding process is useful as a new indicator for the manufacturing error of injection-molded plastic gear. [ABSTRACT FROM AUTHOR]

Helical anchors have been extensively employed as foundation systems for carrying tension loads due to their installation efficiency and large uplift capacity. However, the installation influences of helical anchors are still not well understood, especially for multi-helical anchors. The matrix discrete element method was used to model the process of helical anchor penetration and pull-out in dense sand to investigate the effects of the anchor geometry and advancement ratio (AR, the relative vertical movement per rotation) on soil disturbance, the particle flow mechanism, and the uplift capacity. For shallow helical anchors, the overall disturbance zone is the shape of an inverted cone after installation, while for deep helical anchors, it is funnel-shaped. The advancement ratio has significant effects on the soil particle movement and uplift capacity of helical anchors. The soil particle flow mechanism around helical plates has been identified for single-helix anchors at various advancement ratios, and for double-helix anchors, the influence of the top plate on particle movement during installation was investigated. The uplift capacities of both single- and double-helix anchors increase with the decrease in the AR (AR = 0.5~1), and the influence decreases with the anchor embedment ratio. The efficiency of double-helix anchors induced by installation is close to 1 at pitch-matched installation (AR = 1), indicating that the impact of the top plate during installation is minimal in this case. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of curve called the k-directional Darboux curve. These curves are generated by vector fields that are constructed using the Darboux frame of a given spacelike curve α lying on a timelike surface in Minkowski 3-space E³1 We give the relationships between these curves and their curvatures. In particular, we show how k-directional Darboux curves can be used to classify some special curves, such as helices and slant helices. [ABSTRACT FROM AUTHOR]

The self-assembly of proteins into curved structures plays an important role in many cellular processes. One good example of this phenomenon is observed in the septum-forming protein (SepF), which forms polymerized structures with uniform curvatures. SepF is essential for regulating the thickness of the septum during bacteria cell division. In Bacillus subtilis, SepF polymerization involves two distinct interfaces, the β-β and α-α interfaces, which define the assembly unit and contact interfaces, respectively. However, the mechanism of curvature formation in this step is not yet fully understood. In this study, we employed solid-state NMR (SSNMR) to compare the structures of cyclic wild-type SepF assemblies with linear assemblies resulting from a mutation of G137 on the β-β interface. Our results demonstrate that while the sequence differences arise from the internal assembly unit, the dramatic changes in the shape of the assemblies depend on the α-α interface between the units. We further provide atomic-level insights into how the angular variation of the α2 helix on the α-α interface affects the curvature of the assemblies, using a combination of SSNMR, cryo-electron microscopy, and simulation methods. Our findings shed light on the shape control of protein assemblies and emphasize the importance of interhelical contacts in retaining curvature. [ABSTRACT FROM AUTHOR]

The present work explores the potential for observing multiple reentrant localization behavior in a double-stranded helical (DSH) system, extending beyond the conventional nearest-neighbor hopping (NNH) interaction. The DSH system is considered to have hopping dimerization in each strand, while also being subjected to a transverse electric field. The inclusion of an electric field serves the dual purpose of inducing quasi-periodic disorder and strand-wise staggered site energies. Two reentrant localization regions are identified: one exhibiting true extended behavior in the thermodynamic limit, while the second region shows quasi-extended characteristics with partial spreading within the helix. The DSH system exhibits three distinct single-particle mobility edges linked to localization transitions present in the system. The analysis in this study involves examining various parameters such as the single-particle energy spectrum, inverse participation ratio, local probability amplitude, and more. Our proposal, combining achievable hopping dimerization and induced correlated disorder, presents a unique opportunity to study phenomenon of reentrant localization, generating significant research interest. [ABSTRACT FROM AUTHOR]

Wide band gaps with the propagation of elastic waves at low-frequency are desirable for phononic crystals in many traditional and novel applications. Inspired by the natural helix, we designed a microstructure in a metamaterial plate with an antisymmetric dual helix as the basic local resonant cell. The band structure and displacement transmission curve of metamaterial plates with dual helix cells were calculated by using the finite element method at first, then the band gap characteristics with and without consideration of the mass in the center of the dual helix were compared. The results show that the band gap in the band structure and displacement transmission curves have excellent consistency. Besides, the effects of the parameters including the number of turns of the helix, the plate thickness, and the radius of the attached mass sphere on the band gaps of flexural waves for the metamaterial plate were examined for further evaluation of the potential vibration prohibition application. It is found that the lower frequency of the band gap can be significantly tuned by adding a mass element in the metamaterial plates with dual helix elements, which provides a new method to tune the width of the band gap of a metamaterial plate. [ABSTRACT FROM AUTHOR]

Plant tendril inspired helical structures hold significant promise in various applications. In this study, we advance the understanding of factors influencing the morphology of helical fibers fabricated during co-electrospinning, which is grounded in the mechanism of inducing strain mismatch within the polymer components. Our investigation encompasses a comprehensive analysis of the intrinsic curvature through an updated bilayer strip physical model. Potential factors affecting the resulting curvature of the electrospun helical fibers, including flexibility difference and charge difference within the component pair as well as the evaporation behavior of the chosen solvents for polymers, are explored through numerical simulations and experimental validation. [ABSTRACT FROM AUTHOR]

A new kind of partner curves called osculating mate of a Frenet curve is introduced. Some characterizations for osculating mate are obtained and using the obtained results some special curves such as slant helix, spherical helix, C-slant helix and rectifying curve are constructed. [ABSTRACT FROM AUTHOR]

The involute–evolute pair is a classic theme, which has great research significance in mathematics and engineering. A Cartan null curve is a curve whose tangent vector is light-like on each point, and its module vanishes everywhere along the curve. Due to these special properties of null curves, some research on them shows more particular and interesting prospects. In this paper, the involutes of null Cartan curves are defined and investigated based on the classifications of curves in Minkowski space. The conclusion that the involutes of null Cartan curves only can be space-like is achieved, and the relationships on curvatures, torsions, frames, expressions between a null Cartan curve and its three kinds of space-like involutes are explored. Especially, the pseudo-null involute of a given null Cartan curve can be directly expressed via the structure function of the null curve; the first and second kind space-like involutes of a given null Cartan curve can also be expressed if the tangent distance function is determined. Meanwhile, the k-type null helices and their involutes are expressed by the structure functions of null curves. Last but not least, some typical examples are presented and visualized to characterize such curve pairs explicitly. [ABSTRACT FROM AUTHOR]

This study is based on the discovered relationships between the quaternionic slant helix and the quaternionic general helix. In this direction, we first examined quaternions, spatial quaternionic curves and b-lift curves. Furthermore, we defined the spatial quaternionic b-lift curve and characterized of Frenet fields. Afterward, we found the curvatures of the b-lift curve and using them we obtained a result between the quaternionic slant helix and quaternionic general helix. Finally, we consolidated our results with an example and visualized our curves with the MATLAB program. [ABSTRACT FROM AUTHOR]

In this paper, we focus on general and ζ3-slant helices with any singular points in four-dimensional Euclidean space, which are called framed general and ζ3-slant helices, respectively. Then, we state and prove the conditions of necessity and sufficiency for any framed curves to be general helices or ζ3-slant helices in R4. Also, we give some characterizations for framed helices. [ABSTRACT FROM AUTHOR]

In this paper, we focus on general and ζ3-slant helices with any singular points in four-dimensional Euclidean space, which are called framed general and ζ3-slant helices, respectively. Then, we state and prove the conditions of necessity and sufficiency for any framed curves to be general helices or ζ3-slant helices in R4. Also, we give some characterizations for framed helices. [ABSTRACT FROM AUTHOR]

In this study, we consider framed curves as regular or singular space curves with an adapted frame in Euclidean 3-space. We define framed natural mates of a framed curve that are tangent to the generalized principal normal of the framed curve. Subsequently, we present the relationships between a framed curve and its framed natural mates. In particular, we establish some necessary and sufficient conditions for the framed natural mates of specific framed curves, such as framed spherical curves, framed helices, framed slant helices, and framed rectifying curves. Finally, we support the concept with some examples. [ABSTRACT FROM AUTHOR]

In this paper, we study the developable TN, TB, and NB-Smarandache ruled surface with a pointwise 1-type Gauss map. In particular, we obtain that every developable TN-Smarandache ruled surface has constant mean curvature, and every developable TB-Smarandache ruled surface is minimal if and only if the curve is a plane curve with non-zero curvature or a helix, and every developable NB-Smarandache ruled surface is always plane. We also provide some examples. [ABSTRACT FROM AUTHOR]

The present study discusses bi-null slant helices of (k,m) type in R25 and give the characterization for a curve to be certain (k,m) type bi null slant helix (BNS helix). The discussion includes the proofs for the non existence cases of (k,m) type bi null slant helices in R25. Moreover certain characterizations and non existence have also been obtained for bi null slant helix to be (k,m) type using modified orthogonal frame. [ABSTRACT FROM AUTHOR]

Helices are unique structures that play important roles in biomacromolecules and chiral catalysis. The mechanochemical unfolding of helical structures has attracted the attention of chemists in the past few years. However, it is limited to a few cases which investigated how the mechanochemical reactivity is impacted by helical configurations. No synthetic helical mechanophore is reported. Herein, a Zn (II) bidipyrrin (BDPR‐Zn) double helix is designed as a potential mechanophore. A cyclic olefin containing a doubly strapped BDPR‐Zn is prepared and used for ring‐opening metathesis polymerization. The corresponding polymer is subjected to pulsed ultrasonication for mechanochemical testing. The sonication results reveal the mechanochemical inertness of BDPR‐Zn unit, which is further supported by force‐coupled simulation. Although no obvious activation is observed, our preliminary results on BDPR‐Zn unit could inspire further rational designs on force‐induced helix unfolding. [ABSTRACT FROM AUTHOR]

The present study discusses bi-null slant helices of (k,m) type in R25 and give the characterization for a curve to be certain (k,m) type bi null slant helix (BNS helix). The discussion includes the proofs for the non existence cases of (k,m) type bi null slant helices in R25. Moreover certain characterizations and non existence have also been obtained for bi null slant helix to be (k,m) type using modified orthogonal frame. [ABSTRACT FROM AUTHOR]

A composite material, formed by a cholesteric elastomer slab, doped with randomly but uniformly distributed metallic nano-spheres, is studied. The cholesteric elastomer has a twist jump defect consisting of a finite discontinuity in the helical angle of the structure. The transmittance and reflectance spectra of the elastomer sample are studied when circularly polarized electromagnetic waves are impinging, while it is stretched by the action of an externally imposed agent. It has been observed that the co-polarized and cross-polarized transmittance and reflectance depend on the wavelength of the impinging wave and the amount of metallic spheres parameterized by the filling factor, strain, and magnitude of the twist defect. Additionally, we have found that the position of the line defect within the band reflection is red-shifted either by increasing the filling factor or stretching the sample. [ABSTRACT FROM AUTHOR]

Compared with conventional magnetic ways, modulating a spin-polarized current through electrical means could greatly reduce nano-devices' energy consumption and dimensions, which emerges as a new research area in spintronics. Inspired by the experimental progress on the synthesis of helically twisted graphene, we study the electronic transport of kekulene-like helical graphene nanoribbons through first-principles calculations. By applying a gate voltage, the system can be switched between spin-unpolarized and completely spin-polarized states, realizing an electrically controlled spin filter. Moreover, a fine modulation of the spin polarization can also be achieved, where transmission with any ratio of spin-up to spin-down electrons can be obtained, beyond the traditional spin filter. The analysis shows that it is the particular transmission spectra that play a key role, where two wide peaks with opposite spins reside partially overlapped around the Fermi level. They originate from the p orbitals of the zigzag edge part in the helical structure. Since the configuration only consists of carbon atoms, the electrical control of spin polarization is realized in a pure-carbon nano-system, showing great application potentials. [ABSTRACT FROM AUTHOR]

This survey describes the study of helix (or constant angle) surfaces in different ambient spaces equipped with a Lorentzian metric. We present the study of constant angle surfaces in the Minkowski space, the Lorentzian Heisenberg group, the Lorentzian Berger sphere and some new results the for the 3-dimensional anti-de Sitter space with Berger-like metrics. In every case, we give characterization theorems which describe such surfaces. [ABSTRACT FROM AUTHOR]

The seed metering process of a fluted force-feed seeder was simulated using the Discrete Element Method and its parameters optimized using the Box–Behnken Design of Experiments and the Response Surface Method. The rotational speed of the feed roller, the lead (helix) angle of the flutes, and the number of flutes were the independent variables, while the response value was the seeding uniformity index. Two regression models were investigated, and the following conclusions drawn. For the flute lead angle between 0 and 10 degrees, and the number of flutes between 10 and 14, it was found that the number of flutes and the lead angle influenced the seeding performance the most, with the order of importance being the (i) number of flutes, (ii) lead angle and (iii) roller speed. For the flute lead angle between 5 and 15 degrees, and the number of flutes between 12 and 16, it was found that the roller speed and the number of flutes influenced the seeding performance the most, with the order of importance being the (i) roller speed, (ii) number of flutes and (iii) flute lead angle. The two regression models were then minimized for the seeding uniformity index and the corresponding optima verified experimentally on a conveyor belt test stand fitted with an image recognition system. [ABSTRACT FROM AUTHOR]

In the theory of curves in Euclidean 3-space, it is well known that a curve β is said to be a Bertrand curve if for another curve β⋆ there exists a one-to-one correspondence between β and β⋆ such that both curves have common principal normal line. These curves have been studied in different spaces over a long period of time and found wide application in different areas. In this article, the conditions for a timelike curve to be Bertrand curve are obtained by using a new approach in contrast to the well-known classical approach for Bertrand curves in Minkowski 3-space. Related examples that meet these conditions are given. Moreover, thanks to this new approach, timelike, spacelike and Cartan null Bertrand mates of a timelike general helix have been obtained. [ABSTRACT FROM AUTHOR]

The sound field of a harmonically radiating monopole moving along arbitrary trajectories in three-dimensional space is studied in the frequency range and represented as a convolution integral in Cartesian coordinates. The observation time of the motion of the source can be finite or infinite. This convolution integral is referred to as the "Cartesian Convolution Integral " and is applied to point sources moving on special orbits described by circular and conical helices. For such helical orbits, an alternative approach in cylindrical or spherical coordinates leads to closed form expressions in the form of infinite series for the frequency spectra. The comparison of the results of the Cartesian Convolution Integral with those of the series expansion shows a very good agreement. Finally, the Cartesian Convolution Integral is used to calculate the spectral sound field of a source moving along an elliptical helix. [ABSTRACT FROM AUTHOR]

Gear drive is a common and efficient way to transfer power and motion. To ensure the machining accuracy of gears, the tooth flanks are formed by profile grinding technology in some cases. In the profile grinding process, the calculation of wheels using the information of gears named as the forward-calculation process and obtaining gears based on wheels (the backward-calculation process) traditionally adopt numerical ways. It is always time consuming and large code quantity. To conquer these drawbacks, this article presents an analytical method using the envelope theory to compute the contacting curves that are the basis of getting tooth flanks or wheels in the forward- or the backward-calculation process. For the forward-calculation process, the tooth flank is expressed in the form of an extended straight-line surface that can be taken as the generating line moving along the helix curve. The normal vector for an arbitrary point on the generating line is the same. By using this characteristic, the contacting curve can be explicitly gained as the function of only one parameter. Similarly, in the backward-calculation process, the formed wheel is expressed by a cross section rotating about its axis. For this type of surface, the guide curve is a circle, and the normal vectors of points on the guideline insect with the axis at the same point. Taking advantage of this principle, the contacting curve can be analytically expressed by only one unknown parameter. To verify the validity of the proposed method, some examples and comparative experiments are performed. The results show that the presented method is correct. When compared with the classical numerical way, the time span for the proposed method is 15 times less than that for the numerical way. When compared with the practical grinding wheel and the practical gear, the maximum errors are 0.18 mm and 0.0099 mm, respectively. The proposed method can be served as one of the universal ways to generate formed wheels or involute gears in the profile grinding process. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the spherical indicatrices of a new relationship between Bertrand pair curves in Euclidean 3-space. We obtain necessary and sufficient conditions for this type of Bertrand pair curves to be slant helix, and provide an example. [ABSTRACT FROM AUTHOR]

In a recent paper Tunçer [14] described and examined the moment vectors (T -dual, N-dual, B-dual curve) of the curve with respect to the origin of the vector by using T(s), N(s), B(s) and the position vector of the curve. With the inspiration this paper provided, we define some new associated curves called dual-direction curves as integral curves of a vector field in this study. They are generated with the help of vectorial moments of a space curve in three-dimensional Euclidean space. We attain some connections between the Frenet apparatus of dual-direction curves and main curves. With the help of these dual-direction curves, certain ways to construct helices are determined. Finally, we exemplify these curves with their figures. [ABSTRACT FROM AUTHOR]

In this paper we generalize the notion of helix in the three-dimensional Euclidean space, which we define as that curve α for which there is an F -constant vector field W along α that forms a constant angle with a fixed direction V (called an axis of the helix). We find the natural equation and the geometric integration of helices α where the F -constant vector field W is orthogonal to its axis. [ABSTRACT FROM AUTHOR]

The compression and insulation properties of down are crucial and need to be further explored. This article describes the average number and length of barbs increasing from 67 to 100 and from 11.90 to 26.00 mm with a rise of single down mass, respectively. The mass of a single down is lognormal, and the average value and maximum probability value of individual down mass are 1.46 and 0.62 mg, respectively. There is no significant difference in a helix or b sheet contents through peak deconvolution of the Fourier transform infrared spectroscopy of the barbs and barbules. The compression recovery rates of single down are 58.29% and 58.94% in the x–x and y–y directions, respectively, due to the almost same structure in both directions. Further, the compression recovery rates of down with filling masses of 0.5, 1.0, and 1.5 g decreased by 6.79%, 5.00%, and 7.31% after five consecutive compression cycles, respectively. The thermal conductivity of the down assembly first decreases to 0.024W( m[1 ( ]C[1 and then increased with the compressive deformation, because the relative density and contact points of down fibers are changing. The study into the morphology structure, compression, and thermal properties of down will inspire the design and development of future synthetic insulation materials. [ABSTRACT FROM AUTHOR]

In this paper, we define a nonlinear transformation between space curves which preserves the ratio of t/k of the given curve in 3-dimensional Euclidean space E³. We investigate invariant and associated curves of this transformation by the help of curvature and torsion functions of the base curve. Moreover, we define a new curve (family) so-called quasi-slant helix, and we obtain some characterizations in terms of the curvatures of this curve. Finally, we examine some curves in the kinematics, and give the pictures of some special curves and their images with respect to the transformation. [ABSTRACT FROM AUTHOR]

In this article, a new approach is given for Mannheim curves in 3-dimensional Euclidean space. Thanks to this approach, the necessary and sufficient conditions including the known results have been obtained for a curve to be Mannheim curve in E3. In addition, related examples and graphs are given by showing that Salkowski and anti-Salkowski curves can be the examples of Mannheim curves and their mates. Finally, the Mannheim partner curves are characterized in E3. [ABSTRACT FROM AUTHOR]

The aim of this study is to reveal the relationship between changes in the physical and chemical characterization of eggs during storage and to provide a new way to assess egg freshness at the molecular chemical level. In this study, the Fourier transform infrared (FTIR) spectra of egg albumin from 60 fresh eggs (ISA Brown layer) stored for 1, 10, 20, 30, and 40 days at 4°C and 10°C were measured (n = 6), and the amide I band of the egg albumin spectra was quantified by Fourier deconvolution and curve fitting to obtain the composition of the protein molecular structure. The results showed that different storage temperatures and storage times led to protein denaturation, resulting in changes in the conformation of the protein secondary structure. With increasing storage temperature and storage time, the content of the ordered structures β-sheet and α-helix in the egg protein secondary structure decreased significantly (p < 0.05), and the content of the disordered structure β-turn and random coil increased significantly (p < 0.05). Based on the pattern of protein secondary structure changes during storage, it was found that fresh eggs were better stored at 4°C for up to 15 days. Spearman's correlation analysis of egg protein height, Haugh unit, egg weight, and protein secondary structure in eggs stored at 4°C showed a significant positive correlation between β-sheet and α-helix and egg weight, protein height, and Haugh unit. And a significant negative correlation between random coil and egg weight, protein height, and Haugh unit. Therefore, a curve fitting method based on Fourier transform infrared spectroscopy of deconvoluted spectra is an effective method for evaluating egg quality and freshness. [ABSTRACT FROM AUTHOR]

Aiming to achieve an accurate evaluation of the circumferential position error of the V-shaped apex of double-helical gear, the definition of the V-shaped apex of double-helical gear and the evaluation method of the circumferential position error is studied based on the geometric characteristics of double-helical gear and the definition of shape error. First, the definition of the V-shaped apex of double-helical gear based on the helix and its circumferential position error is presented based on the (American Gear Manufacturers Association) AGMA940-A09 standard. Second, based on the basic parameters, the tooth profile characteristics, and the tooth flank forming principle of double-helical gear, the mathematical model of double-helical gear in a Cartesian space coordinate system is established, and the auxiliary tooth flank and auxiliary helix are constructed to generate some auxiliary measurement points. Finally, the auxiliary measurement points are fitted using the least-squares principle to calculate the position of the V-shaped apex of the double-helical gear in the actual meshing condition and its circumferential position error. The simulation and experimental results show that the simulation results verify the feasibility of the method, and the experimental results (the circumferential position error of the V-shaped apex is 0.0187 mm) are consistent with the results of the literature [Bohui et al., Metrol. Meas. Technol. 36, 33 (2016)]. This method can effectively realize the accurate evaluation of the double-helical gear V-shaped apex position error, providing some guidance for the design and manufacture of double-helical gear. [ABSTRACT FROM AUTHOR]

We are considering the propagation of circularly polarized light normally impinging on a cholesteric elastomer slab doped with metallic spheres. The slab is composed of two layers: the first layer is a right-handed chiral structure, and the second one is a helix with left-handedness; however, the pitch of the chiral structure remains constant. We performed a theoretical model to find numerically, reflection and transmission spectra for circularly polarized light impinging on the slab. We considered the effects of mechanical strains along the helical axis since the force exerted on the structure can tilt the mesogens in the slab along the helical axis. The Photonic Band-Gap(PBG) of the elastomer slab becomes narrowed because of the strain; there we also observe high reflectance (hyper-reflectivity) that depends on the filling factor of the silver doping and on whether the defect is located at a position that contains complete periods of the structure. Additionally, the spectra display reflection bands for both right- and left-polarized light. We expressed the PBG edges in terms of material parameters; this allows us to select the region of the electromagnetic spectrum for the reflection bands. This medium exhibits a hyper-reflective photonic band when the pitches of both right- and left-handed helical layers are identical. [ABSTRACT FROM AUTHOR]

Gluten (Glu) is important to wheat products by forming a three-dimensional matrix. This study aimed to investigate the physicochemical and structural properties of gluten after conjugation with konjac glucomannan (KGM) through the Maillard reaction. The study revealed that the degree of graft increased with the prolonged reaction time. The Glu-KGM conjugates were possessed of increased β-sheet but decreased α-helix and β-turn, as well as unfolding and loose tertiary structures as the reaction proceeded. Among three different proportions, the Glu-KGM 1:1 conjugate was proved to have the most excellent foaming and emulsifying properties, and could form more rigid and firm gelation structures, which could be related to the decreased particle size and increased zeta potential of the conjugate. Overall, the physicochemical and structural properties of gluten were significantly related to the KGM ratios as well as the reaction period. [ABSTRACT FROM AUTHOR]

The transmission of linearly and circularly polarized waves is studied both theoretically and experimentally for chiral metasurfaces formed by arrays of metallic square helices. The helical particles of the metasurfaces are constructed of rectangular bars manufactured by direct three-dimensional printing in solid metals. The transmittance of the metasurface is found to depend critically on the number of bars forming the square helical particles. In the case of an even number of bars, the chiral metasurface exhibits identical co-polarized transmittance of orthogonal linearly polarized waves, which are characterized by a dual-band asymmetric transmission. For an odd number of bars, the metasurface provides the same cross-polarization conversion for any polarization orientation of the incident field and thus serves as a polarization-independent twist polarizer. Finally, the transmittance of this polarizer is investigated with respect to the dimensions of the square helices. The investigated chiral metasurfaces are characterized by strong broadband circular dichroism regardless of the number of bars in the helical particles. The wide variety of transmission properties observed in the metasurfaces makes them particularly attractive for use in polarization conversion and separation devices. [ABSTRACT FROM AUTHOR]

We report a general synthetic route toward helical ladder polymers with varying spring constants, built with chirality‐assisted synthesis (CAS). Under tension and compression, these shape‐persistent structures do not unfold, but rather stretch and compress akin classical Hookean springs. Our synthesis is adaptable to helices with different pitch and diameter, which allowed us to investigate how molecular flexibility in solution depends on the exact geometry of the ladder polymers. Specifically, we showed with molecular dynamic simulations and by measuring the longitudinal 1H NMR relaxation times (T1) for our polymers at different Larmor frequencies, that increasing the helix diameter leads to increased flexibility. Our results present initial design rules for tuning the mechanical properties of intrinsically helical ladder polymers in solution, which will help inspire a new class of robust, spring‐like molecular materials with varying mechanical properties. [ABSTRACT FROM AUTHOR]

Various forms of rational solitons, breathers, rogue wave, periodic wave and multiwave for Davydov solitons in α -helix proteins are described in this paper. We will figure out periodic wave, rogue wave, multiwave, M -shaped solutions, homoclinic breathers, kink cross rational solutions, periodic cross kink, periodic cross rational solitons, generalized breather, Akhmediev breather and Kuznetsov–Ma breather. We will also discuss some interactions between them. At the end, we will provide the graphical representation of our newly discovered solutions. [ABSTRACT FROM AUTHOR]

Approximation of helices has been studied by using in many ways. In this study, it has been examined how a circular helix can be written as Bezier curve and written the 3th degree, 5th degree, and the 7th degree Maclaurin series expansions of helices for the polynomial forms. Hence, they can be written cubic, 5th order, and 7th order Bezier curves, based on the control points with matrix form we have already given in E³. Further we have given the control points of the Bezier curve based on the coefficients of the Maclaurin series expansion of the circular helix. [ABSTRACT FROM AUTHOR]

In the article, the parametric expressions of the dual ruled surfaces are expressed in terms of the vectorial moments of the Frenet vectors. The integral invariants of these surfaces are calculated. It is seen that the dual parts of these invariants can be stated by the real terms. Finally, we present examples of the ruled surfaces with bases such as helix and Viviani’s curves. [ABSTRACT FROM AUTHOR]

In this study, we define spacelike curves in R42 and characterize such curves in terms of Frenet frame. Also, we examine some special spacelike curves of R42, taking into account their curvatures. In addition, we study spacelike slant helices, spacelike B2 slant helices in R42. And then we obtain an approximate solution for spacelike-B2 slant helix. [ABSTRACT FROM AUTHOR]

In the present paper, we give the notion of k-type bi-null Cartan slant helices in R 62, where k ∈ {1, 2, 3, 4, 5, 6}. We give the necessary and sufficient conditions for bi-null Cartan curves to be k-type slant helices in terms of their curvature functions. [ABSTRACT FROM AUTHOR]

In this study, we define spacelike curves in R42 and characterize such curves in terms of Frenet frame. Also, we examine some special spacelike curves of R42, taking into account their curvatures. In addition, we study spacelike slant helices, spacelike B2 slant helices in R42. And then we obtain an approximate solution for spacelike-B2 slant helix. [ABSTRACT FROM AUTHOR]