Intersection Of Curves Research Articles

Economic Activity across Space: A Supply and Demand Approach

What do recent advances in economic geography teach us about the spatial distribution of economic activity? We show that the equilibrium distribution of economic activity can be determined simply by the intersection of labor supply and demand curves. We discuss how to estimate these curves and highlight the importance of global geography—the connections between locations through the trading network—in determining how various policy relevant changes to geography shape the spatial economy.

An enhanced single damage identification in beams using natural frequency shifts and analytic modal curvatures

This article presents an improved procedure for detecting single damage in beam-like structures. Many damage detection methods are based on the analysis of beam natural frequency shifts in damaged and intact states and its analytical modal curvatures. They identify the damage by constructing curves of damage coefficients along the beam and visually determining the point of their mutual intersection. However, for some cases, the absence of an unambiguous point of intersection of these curves or the low accuracy of its localization makes it difficultto use these methods. To accurately determine the mutual intersection of damage coefficient curves, this work proposes to use a subset of modes without one having its curvature close to zero at the site of the alleged damage. This approach greatly simplifies the determination of the point of intersection of the curves of damagecoefficients. An enhanced procedure for the numerical determination of this intersection point is also proposed,rather than the visual one used in existing methods. The effectiveness of the proposed technique was confirmedby numerical simulation followed by experimental verification.

Lower limit of effective reservoir physical properties and controlling factors of medium-deep clastic reservoirs: a case study of the Dawangzhuang area in Raoyang sag, Bohai Bay Basin

With the continuous improvement of oil and gas exploration in the middle and shallow layers, the deep Paleogene in Raoyang sag has become an important exploration field of “increasing reserves and production” in North China. The recognition and control factors of deep effective reservoirs are unclear, which restricts the recognition effect of oil and gas exploration. The key to identify effective reservoirs is to determine the lower limit standard of reservoir physical properties. The single method for calculating the lower limit of physical properties has limitations. The lower limit of the effective reservoir physical properties of the Shahejie Formation in the Dawangzhuang area was obtained by comprehensively using physical property, well logging and oil test data. The data were analysed by oil testing method, metre oil production index test method and frequency curve intersection method. On this basis, combined with the cast thin-section observations, scanning electron microscopy and other test results, the comprehensive control of effective reservoir development of the Shahejie Formation in the Dawangzhuang area of the Raoyang sag was studied from various factors, such as formation pressure, sand body thickness and diagenesis. The results show that the lower limit of porosity was 9.73, 9.44 and 8.85% at depths of Es1, Es2 and Es3, respectively. The lower limit of permeability was 1.21 × 10–3, 1.18 × 10–3 and 0.59 × 10–3 μm2, respectively. Effective reservoirs are easier to form in areas with formation pressure coefficient greater than 1.2. Formation overpressure inhibits compaction and promotes dissolution. The proportion of effective reservoirs of sand bodies with thicknesses greater than 2 m can reach more than 75%. The influence of diagenesis on the reservoir is mainly manifested in compaction and cementation making the reservoir compact. The porosity reduction rate caused by compaction can reach 20–75%, while dissolution makes the reservoir form secondary pores. The average pore throat radius of secondary pores can reach 4 ~ 6.3 µm. This study makes use of the applicability of different methods, which is more instructive for predicting the effective reservoir of the Shahejie Formation in the study area. In addition, the research results provide a reference for the development mechanism of medium-deep clastic reservoirs.

Fractional order-induced bifurcations in a delayed neural network with three neurons.

This paper reports the novel results on fractional order-induced bifurcation of a tri-neuron fractional-order neural network (FONN) with delays and instantaneous self-connections by the intersection of implicit function curves to solve the bifurcation critical point. Firstly, it considers the distribution of the root of the characteristic equation in depth. Subsequently, it views fractional order as the bifurcation parameter and establishes the transversal condition and stability interval. The main novelties of this paper are to systematically analyze the order as a bifurcation parameter and concretely establish the order critical value through an implicit function array, which is a novel idea to solve the critical value. The derived results exhibit that once the value of the fractional order is greater than the bifurcation critical value, the stability of the system will be smashed and Hopf bifurcation will emerge. Ultimately, the validity of the developed key fruits is elucidated via two numerical experiments.

Auto Bias Control Technique for Silicon IQ Modulators Using the Dual-Arms Power Dithers

In high-capacity coherent transmission applications such as 400 Gb/s and beyond, silicon inphase and quadrature modulators (SIQMs) are widely used as a coherent transmitter assembly. The bias points of the SIQM deviate the optimum points because of environmental change. Consequently, auto bias control (ABC) is an essential technique to stabilize the bias points of the SIQM. In this paper, we described a novel method to achieve the bias point high-precision control for SIQMs. First, a pair of the differential power dithers are applied to the dual-arms of the channels I and Q, which can compose a push-pull bias locking mode. By this way, the bias error of the channel P induced by the channels I and Q can be eliminated compared with the conventional single-arm ABC method. Then an orthogonal integration operation is used to extract the dither frequency component of the output signal of the SIQM, and the intersections of the orthogonal-integral curves corresponding to the bias points of the channels I, Q, and P are the optimum bias thermal-power. The simulation and experimental results show that our method exhibits a good performance for locking the optimum thermal-power of the SIQM, and the optical signal-to-noise ratio (OSNR) penalty caused by the proposed method for a 512-Gb/s optical signal transmission with a dual-polarization 16-quadrature amplitude modulation format can be neglected in our experiment.

A novel generating machining process for screw-rotors using an internal-cylindrical skiving cutter on a new CNC skiving machine

To reduce machining time and improve accuracy for producing screw rotors, this study proposes a generating machining process using an internal-cylindrical skiving cutter on a new CNC skiving machine. An internal-barrel rotor is first generated based on a conjugation relationship with a male/female rotor. Then, the cutting edges of the internal-cylindrical skiving cutter are defined by the intersection curves between the rake plane and the barrel rotor surface. A geometrical analysis of the clearance angle allows adjustment of the relative position between the cylindrical cutter and the skived rotor on the cutter's axis. Furthermore, a general model for the skiving process is presented. The result shows that the normal deviations on the skived screw rotors are very close to zero. In addition, a new CNC skiving machine is proposed to perform the cutting process when considering the influence of feed rate. Accordingly, the surface morphology of the skived screw rotor is in the form of micro-size waves arranged in a diagonal structure. Finally, the skived screws surface with a predefined grinding stock is achieved by modifying the cutter geometric.

Persistence of the steady planar normal shock structure in 3‐D unsteady potential flows

AbstractThis paper concerns the dynamic stability of the steady three‐dimensional (3‐D) wave structure of a planar normal shock front intersecting perpendicularly to a planar solid wall for unsteady potential flows. The stability problem can be formulated as a free boundary problem of a quasi‐linear hyperbolic equation of second order in a dihedral‐space domain between the shock front and the solid wall. The key difficulty is brought by the edge singularity of the space domain, the intersection curve between the shock front and the solid wall. Different from the two‐dimensional (2‐D) case, for which the singular part of the boundary is only a point, it is a curve for the 3‐D case in this paper. This difference brings new difficulties to the mathematical analysis of the stability problem. A modified partial hodograph transformation is introduced such that the extension technique developed for the 2‐D case can be employed to establish the well‐posed theory for the initial‐boundary value problem of the linearized hyperbolic equation of second order in a dihedral‐space domain. Moreover, the extension technique is improved in this paper such that loss of regularity in the a priori estimates on the shock front does not occur. Thus, the classical nonlinear iteration scheme can be constructed to prove the existence of the solution to the stability problem, which shows the dynamic stability of the steady planar normal shock without applying the Nash–Moser iteration method.

Geometry Sampling-Based Adaption to DCGAN for 3D Face Generation.

Despite progress in the past decades, 3D shape acquisition techniques are still a threshold for various 3D face-based applications and have therefore attracted extensive research. Moreover, advanced 2D data generation models based on deep networks may not be directly applicable to 3D objects because of the different dimensionality of 2D and 3D data. In this work, we propose two novel sampling methods to represent 3D faces as matrix-like structured data that can better fit deep networks, namely (1) a geometric sampling method for the structured representation of 3D faces based on the intersection of iso-geodesic curves and radial curves, and (2) a depth-like map sampling method using the average depth of grid cells on the front surface. The above sampling methods can bridge the gap between unstructured 3D face models and powerful deep networks for an unsupervised generative 3D face model. In particular, the above approaches can obtain the structured representation of 3D faces, which enables us to adapt the 3D faces to the Deep Convolution Generative Adversarial Network (DCGAN) for 3D face generation to obtain better 3D faces with different expressions. We demonstrated the effectiveness of our generative model by producing a large variety of 3D faces with different expressions using the two novel down-sampling methods mentioned above.

A Graphical Method to Assess the Technical Feasibility of Intentional Islanding of Distributed Synchronous Generators

This article proposes a graphical method to evaluate the feasibility of intentional islanding of distributed synchronous generators. The approach is based on the combination of the performance and restriction curves. These curves are based on the islanding detection capability of the frequency-based protection at the point of common coupling and on the generator protection at its terminals. When relating the islanding detection time, the restriction time and the active power imbalance, the intersection of such curves defines two operating zones: i) the favorable island formation zone, in which the operation of the energized island is stable, and ii) the non-favorable island formation zone, in which the islanding is infeasible. The results showed that the proposed method is a useful tool to adjust and assess frequency-based protection so that an unscheduled islanding event can result in a stable island. In addition, the validation of the results confirmed the coherency of the graphical method.

Inflectionary Invariants for Isolated Complete Intersection Curve Singularities

We investigate the role played by curve singularity germs in the enumeration of inflection points in families of curves acquiring singular members. Let N ≥ 2 N \geq 2 , and consider an isolated complete intersection curve singularity germ f : ( C N , 0 ) → ( C N − 1 , 0 ) f \colon (\mathbb {C}^N,0) \to (\mathbb {C}^{N-1},0) . We define a numerical function m ↦ AD ( 2 ) m ⁡ ( f ) m \mapsto \operatorname {AD}_{(2)}^m(f) that naturally arises when counting m t h m^{\mathrm {th}} -order weight- 2 2 inflection points with ramification sequence ( 0 , … , 0 , 2 ) (0, \dots , 0, 2) in a 1 1 -parameter family of curves acquiring the singularity f = 0 f = 0 , and we compute AD ( 2 ) m ⁡ ( f ) \operatorname {AD}_{(2)}^m(f) for several interesting families of pairs ( f , m ) (f,m) . In particular, for a node defined by f : ( x , y ) ↦ x y f \colon (x,y) \mapsto xy , we prove that AD ( 2 ) m ⁡ ( x y ) = ( m + 1 4 ) , \operatorname {AD}_{(2)}^m(xy) = {{m+1} \choose 4}, and we deduce as a corollary that AD ( 2 ) m ⁡ ( f ) ≥ ( mult 0 ⁡ Δ f ) ⋅ ( m + 1 4 ) \operatorname {AD}_{(2)}^m(f) \geq (\operatorname {mult}_0 \Delta _f) \cdot {{m+1} \choose 4} for any f f , where mult 0 ⁡ Δ f \operatorname {mult}_0 \Delta _f is the multiplicity of the discriminant Δ f \Delta _f at the origin in the deformation space. Significantly, we prove that the function m ↦ AD ( 2 ) m ⁡ ( f ) − ( mult 0 ⁡ Δ f ) ⋅ ( m + 1 4 ) m \mapsto \operatorname {AD}_{(2)}^m(f) -(\operatorname {mult}_0 \Delta _f) \cdot {{m+1} \choose 4} is an analytic invariant measuring how much the singularity “counts as” an inflection point. We prove similar results for weight- 2 2 inflection points with ramification sequence ( 0 , … , 0 , 1 , 1 ) (0, \dots , 0, 1,1) and for weight- 1 1 inflection points, and we apply our results to solve a number of related enumerative problems.

Unlikely intersections of curves with algebraic subgroups in semiabelian varieties

Let G be a semiabelian variety and C a curve in G that is not contained in a proper algebraic subgroup of G. In this situation, conjectures of Pink and Zilber imply that there are at most finitely many points contained in the so-called unlikely intersections of C with subgroups of codimension at least 2. In this note, we establish this assertion for general semiabelian varieties over overline{mathbb {Q}}. This extends results of Maurin and Bombieri, Habegger, Masser, and Zannier in the toric case as well as Habegger and Pila in the abelian case.

Fracture Closure Empirical Model and Theoretical Damage Model of Rock under Compression.

The rock or rock mass in engineering often contains joints, fractures, voids, and other defects, which are the root cause of local or overall failure. In response to most of the current constitutive models that fail to simulate the nonlinear fracture compaction deformation in the whole process of rock failure, especially brittle rocks, a piecewise constitutive model was proposed to represent the global constitutive relation of rocks in this study, which was composed of the fracture compaction empirical model and the damage statistical constitutive model. The fracture empirical compaction model was determined by fitting the expressions of fracture closure curves of various rocks, while the rock damage evolution equation was derived underpinned by the fracture growth. According to the effective stress concept and strain equivalence hypothesis, the rock damage constitutive model was deduced. The model parameters of the fracture compaction empirical model and damage statistical constitutive model were all calculated by the geometrical characteristics of the global axial stress-strain curve to guarantee that the models are continuous and smooth at the curve intersection, which is also simple and ready to program. Finally, the uniaxial compression test data and the triaxial compression test data of different rocks in previous studies were employed to validate the models, and the determination coefficient was used to measure the accuracy. The results showed great consistency between the model curves and test data, especially in the pre-peak stage.

Gradeability of a Forwarder Based on Traction Performance

Based on the knowledge of the dimensional and mass features of a forwarder, a model was developed to assess its mobility during timber forwarding uphill in a safe and eco-efficient way. The model is based on knowledge of the position of the forwarder’s centre of gravity, its declared payload and the length of the loaded timber, as well as the gradeability for uphill timber forwarding based on the traction characteristics of the vehicle. The model connects two research approaches, (1) vehicle–terrain approach (distribution of axle loads depending on the longitudinal terrain slope) and (2) wheel–soil approach (estimation of the traction characteristics of the forwarder based on the wheel numeric), concerning previous research: (i) underload on the front axle of the vehicle, (ii) overload on the rear axle of the vehicle, (iii) permissible tire load, (iv) minimal soil bearing capacity, (v) wheel slip. Simulation modelling for the assessment of the forwarders’ mobility range during timber forwarding uphill was conducted on an example of an eight-wheel Komatsu 875 forwarder, with a declared payload of 16,000 kg, equipped with 710/45-26.5 tires, for which the position of the centre of gravity was determined by the method of lifting the axle. The results of the distribution of the adhesion load on the front and rear axles of the forwarder indicated that, during timber forwarding of 16,000 kg and 4.82 m long hardwood logs on a terrain slope below 68%, there is no critical unloading on the front bogie axle, nor overloading on the rear bogie axle, i.e., wheel tire overload that could limit forwarder mobility. For the specified range of longitudinal terrain slope, a minimal cone index of 950 kPa for an exemplary forwarder is an environmental factor and was calculated based on the nominal ground pressure of the reference (heavier loaded) rear wheels of the vehicle. The forwarders’ mobility range was determined by the intersection curves of the gradeability (based on forwarders’ traction characteristics at wheel slip of 25% vs. cone index) and the curve of the minimal soil cone index.

Изучение реакции ионов Cu(II) с N-(бензоил)-N'-(фенилсульфонил)гидразином в аммиачных средах спектрофотометрическим методом

The reaction of complexation of N-(benzoyl)-N'-(phenylsulfonyl)hydrazine with Cu(II) ions in an ammonia medium has been studied. The absorption spectra of the reagent and its complex with Cu(II) ions have been recorded and analyzed. The optimal conditions for the formation of the complex compound were found: the pH range of complex formation; optimal time for color development; amount of photometric reagent. Under optimal conditions for the complex formation of BPSH with Cu(II) ions, a calibration graph was constructed. The Bouguer-Lambert-Beer law is fulfilled in the range from 0,5 to 1,75 mg Cu(II) in 25 ml of solution. The true (19389) and apparent (4708) molar light absorption coefficients were calculated. The methods of saturation, equilibrium shift, curve intersection, isomolar series, and conductometric titration were used to determine the molar ratios in a solution of a complex compound – [Сu(II)]:[BFSH] = 1:1 and 1:2. According to the Babko method, the conditional stability constant of the complex was calculated – 2,45∙1013. The convergence and correctness of the spectrophotometric technique were determined by the method of mathematical statistics.

Planar Sections of a Surface Close to an Umbilic

We study the intersection between a smooth algebraic surface with an umbilic point and a plane parallel and close to the tangent plane at the umbilic. The problem has its origin in the study of isophote (equal illumination) curves in a 2-dimensional image. In particular, we study the circles which have exceptional tangency to this intersection curve: ordinary tangency at one point and osculating at another; ordinary tangency at three points; and 4-point tangency at a vertex. The centres of circles having ordinary tangency at two points trace out a curve whose closure is the symmetry set of the intersection curve, and the exceptional circles above give respectively cusps, triple crossings and endpoints of this set. We analyse the curves traced out by the contact points and centres of the exceptional circles as the plane approaches the tangent plane at the umbilic. We also briefly discuss the global structure of the symmetry set by means of a typical example.

Formulation of SH wave characteristics in nonlocal nanoplates

AbstractThe scale effect of mechanical properties is one of the most critical issues in application of the nanostructures. In order to study the scale effect on SH waves in nanoplates, a Legendre polynomial series method combined with the nonlocal theory (N‐LPSA) is developed in this paper. The presented method enables the boundary condition achieved quickly by the derived iterative solution formula of the integral, which contains nonlocal factors and Legendre polynomials. Besides, the formula of escape frequency is deduced analytically to facilitate the study of wave propagation law. Numerical comparisons show the correctness of the N‐LPSA. The results indicate that cut‐off frequencies of some higher‐order modes are higher than their escape frequencies. The anisotropy with the nonlocal effects can lead to the intersection of the modal curves, which does not appear in classical structures. Moreover, the fitting formulas of cut‐off and crossing frequencies are developed to predict the compression and the intersection of the modal curves, respectively.

Exploring the Optimal Curves of Intersection for Enhanced 3D Shape Designing A Comprehensive Study on Geometric Optimization Techniques

Surface and solid intersection is emerging swiftly in many applications of computer graphics, engineering and mathematical models. In engineering science, several algorithms are produced for some unique purposes like intersection of prism/cone, cone/cone, prism/cylinder etc. All such procedures used different 3D drawing tools for creating geometrical interpretation of their required models. Surface intersection deals with numerous algorithms in computational and applied mathematics, needed for intersection of different surfaces such as rational polynomial parametric, implicit algebraic etc. In this paper, a novel surface intersection approach is proposed which works for all types of intersection like; parametric-parametric, explicit-explicit, implicit-explicit surfaces. This scheme includes a method for determination of significant points (boundary and turning points) from surface intersection sequence points. Optimal curve is fitted to these points by rational quadratic spline and a soft computing technique Genetic Algorithm (GA) is applied for attaining optimized curve, by allotting specific shape parameter values in the depiction of rational quadratic spline. However, some experimental results show the efficiency and robustness of this technique.

Topological Classification and Determination of Non-Degenerate Intersections of Two Dupin Cyclides

The surface-surface intersection is a fundamental task in CAD/CAM. We present the classification and a full enumeration of the topology of all non-degenerate intersections of two Dupin cyclides. Inversion geometry is first used to transform the intersection of two Dupin cyclides to that of a cyclide and a torus. Then the topology of the intersection curve is reduced to the arrangements of the main circle of the torus and another pair of circles, which can be characterized by a simple algebraic sequence. Based on the classification and enumeration results, an efficient determination algorithm for the topology of two Dupin cyclides is also provided. • A classification of the non-degenerate intersections of two Dupin cyclides is given by a simple algebraic sequence. • A full enumeration of all non-degenerate intersections of two Dupin cyclides based on a simple algebraic sequence is provided. • An efficient and robust algorithm of determining the inter- section topology of two Dupin cyclides is provided.

On dispersion curve coloring for mechanical metafilters

This paper formalizes smooth curve coloring (i.e., curve identification) in the presence of curve intersections as an optimization problem, and investigates theoretically properties of its optimal solution. Moreover, it presents a novel automatic technique for solving such a problem. Formally, the proposed algorithm aims at minimizing the summation of the total variations over a given interval of the first derivatives of all the labeled curves, written as functions of a scalar parameter. The algorithm is based on a first-order finite difference approximation of the curves and a sequence of prediction/correction steps. At each step, the predicted points are attributed to the subsequently observed points of the curves by solving an Euclidean bipartite matching subproblem. A comparison with a more computationally expensive dynamic programming technique is presented. The proposed algorithm is applied with success to elastic periodic metamaterials for the realization of high-performance mechanical metafilters. Its output is shown to be in excellent agreement with desirable smoothness and periodicity properties of the metafilter dispersion curves. Possible developments, including those based on machine-learning techniques, are pointed out.

Monodromy of Kodaira fibrations of genus 3

AbstractA Kodaira fibration is a non‐isotrivial fibration from a smooth algebraic surface S to a smooth algebraic curve B such that all fibers are smooth algebraic curves of genus g. Such fibrations arise as complete curves inside the moduli space of genus g algebraic curves. We investigate here the possible connected monodromy groups of a Kodaira fibration in the case and classify which such groups can arise from a Kodaira fibration obtained as a general complete intersection curve inside a subvariety of parametrizing curves whose Jacobians have extra endomorphisms.