Academic literature on the topic 'Algorytm Shanksa'

Shanks' transformation is a well know sequence transformation for accelerating the convergence of scalar sequences. It has been extended to the case of sequences of vectors and sequences of square matrices satisfying a linear difference equation with scalar coefficients. In this paper, a more general extension to the matrix case where the matrices can be rectangular and satisfy a difference equation with matrix coefficients is proposed and studied. In the particular case of square matrices, the new transformation can be recursively implemented by the matrix $\varepsilon$-algorithm of Wynn. Then, the transformation is related to matrix Pad\'{e}-type and Pad\'{e} approximants. Numerical experiments showing the interest of this transformation end the paper.

We present a polynomial-time parsing algorithm for CCG, based on a new decomposition of derivations into small, shareable parts. Our algorithm has the same asymptotic complexity, O( n6), as a previous algorithm by Vijay-Shanker and Weir (1993), but is easier to understand, implement, and prove correct.

BACKGROUND: Kaposi’s sarcoma was first described in 1872 by Moritz Kaposi. To date, it is considered a malignant disease is originating from the endothelial cells of the lymphatic vessels believed to be infected with HHV-8. The current classification defines four major epidemiological forms of Kaposi’s sarcoma: classical, endemic, AIDS-associated, and iatrogenic. CASE REPORT: A 90-year-old male is presented with multiple plaques- and tumour-shaped brown-violet formations located on an erythematous-livid base in the area of both feet and both shanks. Two samples were taken from the lesions on the skin of the shanks, with histopathological examination and the subsequent immunohistochemistry showing Kaposi’s sarcoma. CONCLUSIONS: Kaposi sarcoma is a disease that causes difficulties both in diagnostic and therapeutic respect. The only sure way to determine the correct diagnosis is immunohistochemical staining with the anti-HHV8 antibody. Despite the wide range of systematic and local treatment options, there is still no unified algorithm and a unified strategy for the treatment of Kaposi’s sarcoma.

We study the parsing complexity of Combinatory Categorial Grammar (CCG) in the formalism of Vijay-Shanker and Weir ( 1994 ). As our main result, we prove that any parsing algorithm for this formalism will take in the worst case exponential time when the size of the grammar, and not only the length of the input sentence, is included in the analysis. This sets the formalism of Vijay-Shanker and Weir ( 1994 ) apart from weakly equivalent formalisms such as Tree Adjoining Grammar, for which parsing can be performed in time polynomial in the combined size of grammar and input sentence. Our results contribute to a refined understanding of the class of mildly context-sensitive grammars, and inform the search for new, mildly context-sensitive versions of CCG.

For any square-free polynomial D over a finite field of characteristic at least 5, we present an algorithm for generating all cubic function fields of discriminant D. We also provide a count of all these fields according to their splitting at infinity. When D′ = D/(-3) has even degree and a leading coefficient that is a square, i.e. D′ is the discriminant of a real quadratic function field, this method makes use of the infrastructures of this field. This infrastructure method was first proposed by Shanks for cubic number fields in an unpublished manuscript from the late 1980s. While the mathematical ingredients of our construction are largely classical, our algorithm has the major computational advantage of finding very small minimal polynomials for the fields in question.

This study aimed to investigate the performance of an updated version of our pre-impact detection algorithm parsing out the output of a set of Inertial Measurement Units (IMUs) placed on lower limbs and designed to recognize signs of lack of balance due to tripping. Eight young subjects were asked to manage tripping events while walking on a treadmill. An adaptive threshold-based algorithm, relying on a pool of adaptive oscillators, was tuned to identify abrupt kinematics modifications during tripping. Inputs of the algorithm were the elevation angles of lower limb segments, as estimated by IMUs located on thighs, shanks and feet. The results showed that the proposed algorithm can identify a lack of balance in about 0.37 ± 0.11 s after the onset of the perturbation, with a low percentage of false alarms (<10%), by using only data related to the perturbed shank. The proposed algorithm can hence be considered a multi-purpose tool to identify different perturbations (i.e., slippage and tripping). In this respect, it can be implemented for different wearable applications (e.g., smart garments or wearable robots) and adopted during daily life activities to enable on-demand injury prevention systems prior to fall impacts.

Elliptic curves were first proposed as a basis for public key cryptography in the mid 1980's. They provide public key cryptosystems based on the difficulty of the elliptic curve discrete logarithm problem (ECDLP) , which is so called because of its similarity to the discrete logarithm problem (DLP) over the integers modulo a large prime. One benefit of elliptic curve cryptosystems (ECCs) is that they can use a much shorter key length than other public key cryptosystems to provide an equivalent level of security. For example, 160 bit ECCs are believed to provide about the same level of security as 1024 bit RSA. Also, the level of security provided by an ECC increases faster with key size than for integer based discrete logarithm (dl) or RSA cryptosystems. ECCs can also provide a faster implementation than RSA or dl systems, and use less bandwidth and power. These issues can be crucial in lightweight applications such as smart cards. In the last few years, ECCs have been included or proposed for inclusion in internationally recognized standards. Thus elliptic curve cryptography is set to become an integral part of lightweight applications in the immediate future. This thesis presents an analysis of several important issues for ECCs on lightweight devices. It begins with an introduction to elliptic curves and the algorithms required to implement an ECC. It then gives an analysis of the speed, code size and memory usage of various possible implementation options. Enough details are presented to enable an implementer to choose for implementation those algorithms which give the greatest speed whilst conforming to the code size and ram restrictions of a particular lightweight device. Recommendations are made for new functions to be included on coprocessors for lightweight devices to support ECC implementations Another issue of concern for implementers is the side-channel attacks that have recently been proposed. They obtain information about the cryptosystem by measuring side-channel information such as power consumption and processing time and the information is then used to break implementations that have not incorporated appropriate defences. A new method of defence to protect an implementation from the simple power analysis (spa) method of attack is presented in this thesis. It requires 44% fewer additions and 11% more doublings than the commonly recommended defence of performing a point addition in every loop of the binary scalar multiplication algorithm. The algorithm forms a contribution to the current range of possible spa defences which has a good speed but low memory usage. Another topic of paramount importance to ECCs for lightweight applications is whether the security of fixed curves is equivalent to that of random curves. Because of the inability of lightweight devices to generate secure random curves, fixed curves are used in such devices. These curves provide the additional advantage of requiring less bandwidth, code size and processing time. However, it is intuitively obvious that a large precomputation to aid in the breaking of the elliptic curve discrete logarithm problem (ECDLP) can be made for a fixed curve which would be unavailable for a random curve. Therefore, it would appear that fixed curves are less secure than random curves, but quantifying the loss of security is much more difficult. The thesis performs an examination of fixed curve security taking this observation into account, and includes a definition of equivalent security and an analysis of a variation of Pollard's rho method where computations from solutions of previous ECDLPs can be used to solve subsequent ECDLPs on the same curve. A lower bound on the expected time to solve such ECDLPs using this method is presented, as well as an approximation of the expected time remaining to solve an ECDLP when a given size of precomputation is available. It is concluded that adding a total of 11 bits to the size of a fixed curve provides an equivalent level of security compared to random curves. The final part of the thesis deals with proofs of security of key exchange protocols in the Canetti-Krawczyk proof model. This model has been used since it offers the advantage of a modular proof with reusable components. Firstly a password-based authentication mechanism and its security proof are discussed, followed by an analysis of the use of the authentication mechanism in key exchange protocols. The Canetti-Krawczyk model is then used to examine secure tripartite (three party) key exchange protocols. Tripartite key exchange protocols are particularly suited to ECCs because of the availability of bilinear mappings on elliptic curves, which allow more efficient tripartite key exchange protocols.

This chapter deals with two related problems occurring frequently in the physical sciences: first, the problem of estimating the value of a function from a limited number of data points; and second, the problem of calculating its value from a series approximation. Numerical methods for interpolating and extrapolating data are presented. The famous Lagrange interpolating polynomial is introduced and applied to one-dimensional and multidimensional problems. Cubic spline interpolation is introduced and an implementation in terms of Eigen classes is given. Several techniques for improving the convergence of Taylor series are discussed, including Shank’s transformation, Richardson extrapolation, and the use of Padé approximants. Conversion between representations with the quotient-difference algorithm is discussed. The exercises explore public transportation, human vision, the wine market, and SU(2) lattice gauge theory, among other topics.

Abstract In the turning operation chatter or vibration is a frequent problem, which affects the result of the machining, and, in particular, the surface finish. Tool life is also influenced by vibration. Severe acoustic noise in the working environment frequently occurs as a result of dynamic motion between the cutting tool and the workpiece. These problems can be reduced by active control of machine-tool vibration. Adaptive feedback control based on the filtered-x LMS-algorithm, enables a reduction of the vibration by up to 40 dB at 1.5 kHz and by approximately 40 dB at 3 kHz. The active control performed a broadband attenuation of the sound pressure level by up to 35 dB. A significant improvement of the work-piece surface was also observed. In the active control of tool vibration a tool holder construction based on integrated high magnetostrictive actuators was used. However, both the physical features and properties of a active tool holder construction based on high magnetostrictive actuators and the fact that this type of actuators generally have a non-linear behaviour highly reduce its applicability to the general lathe and turning operation. Therefor, a new generation embedded active tool holder shanks based on piezo ceramic actuators have been developed. Based on spectrum estimates, both coherence spectrum and frequency response function estimates has been calculated for both the old tool holder construction and the new generation active tool holder shank. From the results it follows that the phase delay is smaller and the linearity of the new generation active tool holder shank are superior compared to the old technology. It is also obvious that physical features and properties of new generation embedded active tool holder shanks based on piezo ceramic actuators fits the general lathe application.

This paper presents the optimization design of a high bypass ratio civil fan blade with the consideration of aerodynamics, static and dynamic mechanics. The baseline fan blade was designed with a conventional approach without using automatic optimization techniques on both the aero side and the mechanical side. Therefore, the objective of this paper is to achieve a higher aero-mechanical performance under the multiple aerodynamic and mechanical constraints. Before the optimization, the static stress and modal analysis are performed on the baseline fan blade with/without the introduction of the arc dovetail root and shank. The results are compared to investigate the necessity of including the arc root and shank in the aero-mechanical optimization. With respect to the optimization process, the numerical design of experiment (DOE) by means of high fidelity CFD/FEA computations is firstly performed to construct the database for the initialization of Kriging surrogate mode. After that, the surrogate model is integrated with the optimization design process, and the non-dominated sorting genetic algorithm (NSGAII) is implemented to obtain the Pareto front, based on which the optimal design is selected. Utilizing this optimization process, both the aero-only and aero-mechanical optimizations are carried out. The results show that the attenuation of the 3D shock wave strength between the middle and shroud span improves the overall aero performance of the fan blade in both the aero-only optimal design and the aero-mechanical optimal design. Compared with the aero-only optimal design, the aero-mechanical optimal design shows the efficiency penalty within all the operation range simulated, however, the mechanical performance is significantly enhanced by the mitigation of the static stress level on the entire arc dovetail root and shank as well as the increase of the resonance margin.

Abstract A modified Euler angles method, dual Euler angles approach, has been proposed to describe exact joint motion. In the dual Euler angles method, joint motion is considered as three successive screw motions with respect to the axes of the moving segment coordinate system and the screw motion displacements are represented by dual angles accordingly. The algorithm for calculating dual Euler angles from coordinates of markers on joint segments has also been provided. In this paper, the dual Euler angles method is applied to describe the motion of ankle joint during dorsiflexion-plantarflexion. Due to the difficulty in tracking the motion of the talus segment in vivo, only the overall motion of the ankle-subtalar complex, that is, the relative motion of the foot with respect to the shank, was measured in the present study.

This paper presents optimization schemes for the five-axis flank milling of jet engine impellers based on the mechanics model explained in Part I. The process is optimized by varying the feed automatically as the tool-workpiece engagements, i.e. the process, varies along the tool path. The feed is adjusted by limiting feed-dependent peak outputs to a set of user-defined constraints. These outputs are tool shank bending stress, tool deflection, maximum chip load (to avoid edge chipping) and the torque limit of the machine. The linear and angular feeds of the machine are optimized by two different methods — a multi-constraint based virtual adaptive control of the process and a non-linear root finding algorithm. The five-axis milling process is simulated in a virtual environment, and the resulting process outputs are stored at each position along the tool path. The process is recursively fitted to a first order process with a time varying gain and a fixed time constant, and a simple Proportional Integral controller is adaptively tuned to operate the machine at threshold levels by manipulating the feedrate. As an alternative to virtual adaptive process control, the feedrate is optimized by a non-linear root-finding algorithm. The optimum feed is solved for iteratively, respecting tool stress, tool deflection, torque and chip load constraints, using a non-linear root finding algorithm. Both methods are shown to produce almost identical optimized feed rate profiles for the roughing tool path discussed in Part I of the paper. The new feed rate profiles are shown to considerably reduce the cycle time of the impeller while avoiding process faults that may damage the part or the machine.

A two-degree-of-freedom (2-DOF) model comprising nonlinear delay differential equations (DDEs) is analyzed for self-excited oscillations during orthogonal turning. The model includes multiple time delays, possibility of tool leaving cut, additional process damping (due to flank interference), ploughing force, and shear-angle/friction-angle variation. An algorithm, based on an existing shooting method for DDEs, is developed to simulate tool dynamics and seek periodic solutions. The multiple-regenerative and tool-leaving-cut effects are simulated via an equivalent 1-DOF system by introducing a time shift. While the limit cycle amplitude and minimum-period obtained via shooting and via direct numerical integration compare well, the latter method converges very slowly, thus establishing the efficiency of the former. Numerical studies involving the machining parameters are presented. Only period-1 motion was observed for the range of cutting parameters considered here. Features of a subcritical Hopf bifurcation appear in the amplitude versus width-of-cut plane. This implies the possibility of subcritical instability characterized by sudden onset of finite-amplitude chatter. Additional process damping causes a reduction in chatter amplitudes as well as the subcritical instability to occur at a larger width of cut. An increase in width of cut causes frequent tool-leaving-cut events and increased chatter amplitudes. The frequency of tool disengagement increases with cutting velocity, despite cutting force in the shank direction remaining constant over a certain velocity range. The chatter amplitude at first increases and then decreases when the cutting velocity or the uncut chip thickness is increased. The present plant model and dynamics could be useful for real time active control of tool chatter.