Multivector Research Articles

Optimal Scheduling of Multi Vector Energy Networks Considering Resiliency Improvement

Optimal Scheduling of Multi Vector Energy Networks Considering Resiliency Improvement

Logarithm of multivector in real 3D Clifford algebras

Closed form expressions for a logarithm of general multivector (MV) in basis-free form in real geometric algebras (GAs) Clp,q are presented for all n = p + q = 3. In contrast to logarithm of complex numbers (isomorphic to Cl0,1), 3D logarithmic functions, due to appearance of two double angle arc tangent functions, allow to include two sets of sheets characterized by discrete coefficients. Formulas for generic and special cases of individual blades and their combinations are provided.

Социальная безопасность как условие воспроизводства территориальных систем в приграничных регионах

In modern conditions, local territorial systems are undergoing serious transformations. The major vectors of the evolution of most communities and local societies nowadays are the increasing complexity of technological infrastructure and its expansion into absolutely all spheres of life, as well as the awareness of the costs and risks of globalization and the desire to avoid them by modeling local and national identity with the actualization and ideologization of traditional values (religious, ethno-cultural, etc.), which is usually of a highly conflictual nature. These multi–vector and often unmanageable transformations dramatically increase the level of risks and threats at various levels – from global to local – and pose the task of forming a new architecture for man-aging territorial systems, built taking into account regional conditions. It is emphasized that all socio-territorial systems in border regions are being transformed due to the increase of military and political threats, which en-tails changes in the axiosphere of residents. Social security becomes a priority, which can be ensured through the consolidation of efforts of government and civilian structures.

Exponentials of general multivector in 3D Clifford algebras

Closed form expressions to calculate the exponential of a general multivector (MV) in Clifford geometric algebras (GAs) Clp;q are presented for n = p + q = 3. The obtained exponential formulas were applied to find exact GA trigonometric and hyperbolic functions of MV argument. We have verified that the presented exact formulas are in accord with series expansion of MV hyperbolic and trigonometric functions. The exponentials may be applied to solve GA differential equations, in signal and image processing, automatic control and robotics.

Arranging university semester date to minimize annual CO2 emission: A UK university case study

SummaryExisting methods of reducing carbon emissions on campus often require substantial investment, and the potential opportunities for carbon dioxide and energy savings in universities with existing infrastructure have not been considered in much detail. This work fills this gap by considering an indirect and soft demand response strategy, i.e., semester arrangement. To identify the optimal operational strategy of a realistic campus-level multi vector energy system (MES) in Scotland based on CO2 emissions, an original tool is presented. Two conclusions can be drawn safely from the case study. Firstly, changing the operational mode of the university could significantly reduce CO2 emissions. Secondly, considering the difference between average emission factor (AEF) and marginal emission factor (MEF) in the power grid, the different operational modes will bring different electricity/heat demands and also affect carbon emissions. The work opens up a new perspective for worldwide university operators who are considering reducing CO2 emissions.

Square root of a multivector in 3D Clifford algebras

The problem of square root of multivector (MV) in real 3D (n = 3) Clifford algebras Cl3;0, Cl2;1, Cl1;2 and Cl0;3 is considered. It is shown that the square root of general 3D MV can be extracted in radicals. Also, the article presents basis-free roots of MV grades such as scalars, vectors, bivectors, pseudoscalars and their combinations, which may be useful in applied Clifford algebras. It is shown that in mentioned Clifford algebras, there appear isolated square roots and continuum of roots on hypersurfaces (infinitely many roots). Possible numerical methods to extract square root from the MV are discussed too. As an illustration, the Riccati equation formulated in terms of Clifford algebra is solved.

EEG-based epileptic seizure detection using GPLV model and multi support vector machine

Epilepsy is chronic neurological disorder that is clinically detected by continuous monitoring of Electroencephalogram (EEG) signals by experienced clinicians. Epilepsy is detected by clinicians based on the visual observation of EEG records that normally consumes more time and sensitive to noise. To address these issues, a new system is proposed for automatic epileptic seizure recognition. Gaussian Process Latent Variable Model (GPLVM) is used to lessen the number of features by achieving a set of principal features that significantly rejects the “curse of dimensionality” concern. Then, a supervised classifier (Multi Support Vector Machine (MSVM)) is used to classify the epileptic seizure classes such as normal, ictal, and interictal. Experimental result exemplifies that the proposed work effectively classifies the epileptic seizure classes in light of sensitivity, specificity, False Positive Rate (FPR), False Negative Rate (FNR), and accuracy. The proposed work improves the classification accuracy upto 2.5-12% related to the existing works. The proposed work delivers a new avenue for assisting clinicians in diagnosing epileptic seizure.

МНОГОВЕКТОРНАЯ ПРОМЫШЛЕННАЯ ПОЛИТИКА РОССИИ В УСЛОВИЯХ ФОРМИРОВАНИЯ НОВОГО ИНДУСТРИАЛЬНОГО ЛАНДШАФТА

МНОГОВЕКТОРНАЯ ПРОМЫШЛЕННАЯ ПОЛИТИКА РОССИИ В УСЛОВИЯХ ФОРМИРОВАНИЯ НОВОГО ИНДУСТРИАЛЬНОГО ЛАНДШАФТА

MPTC of a six-phase PMSHM with auxiliary voltage vectors

Permanent magnet synchronous hub motors (PMSHMs) have been gradually introduced into the applications of electric vehicles. In order to output more torque, many researchers turned their research direction to six-phase motors. Because it is composed of two sets of three-phase windings, there will be interference between the windings, affecting the performance of the motor. In order to improve the steady and dynamic-state performance of permanent magnet six phase synchronous motor, a predictive torque control method based on multi vector model is proposed in this paper. Finally, experimental results show the effectiveness of this method.

State Policy of Ukraine in the Context of its European Integration

The article examines the peculiarities of the formation of Ukraine’s state policy on European integration from the beginning of independence in 1991 to the present day. After a brief analysis of Ukraine’s state policy throughout the period of independence, the main emphasis is made on the current stage of development of Ukraine’s relations with the EU – after the Revolution of Dignity in 2014. It is shown that after the events of 2014, the state policy of Ukraine, which is aimed at integration with the EU, is qualitatively transformed and intensified. It is shown that the objectivity of the European direction of Ukraine’s foreign policy is logically conditioned by the geopolitical position and history of our state. The article analyzes the principles and trends in relations between Ukraine and the European Union, analyzes the most important stages and events that define the dialogue of our country with this international structure. Important integration factors are commitment to European values and European identity. In Ukraine, despite official statements about European integration as a foreign policy priority, the political elite does not always demonstrate consistency in the implementation of a certain foreign policy course. The success of the European integration strategy will depend on the implementation of reforms, norms and rules of the EU It has been proved that since the beginning of Ukraine’s independence, the real intensification of the state policy aimed at Ukraine’s European integration has intensified after the Revolution of Dignity. The high level of public support for the eropean inegration shows how much the situation in Ukraine has changed since 2014. Such events as the Euromaidan, Russia’s annexation of Crimea, the war in Donbass and Western sanctions against the Russian Federation have forced Ukraine to move away from its former multi–vector foreign policy. between the West and Moscow. Today, Ukraine’s cooperation with the EU is developing in all major priority areas, covering the economic, political, social and military sectors. The course for European integration follows from the very nature of Ukraine’s state independence, its desire to become an integral part of Europe.

Многовекторность формата заявления (жанрово-репрезентативные особенности)

Многовекторность формата заявления (жанрово-репрезентативные особенности)

THE MULTI–VECTOR RESEARCH IN THE EXPLORATION OF MINERAL DEPOSITS Abstract. A spatial analysis of the curvature of exploration wells was carried out. Ways of replacement of the actual bore axis broken line. Keywords: coal seam, exploratory well, d

THE MULTI–VECTOR RESEARCH IN THE EXPLORATION OF MINERAL DEPOSITS Abstract. A spatial analysis of the curvature of exploration wells was carried out. Ways of replacement of the actual bore axis broken line. Keywords: coal seam, exploratory well, d

FFT-ETM based distortion less and high payload image steganography

This paper is presenting a novel high capacity based imperceptible and robust image steganography technique for obscured communication. A considerable literature studied on this domain reveals distortion that drastically affects image quality. These techniques obscure covert data in most significant bits or least significant bits of host image via easy or unsystematic replacement. Such schemes are vulnerable to malevolent attacks like sample pair method, chi-square test, and quality of host image especially badly affected by MSB replacement. Furthermore, such schemes are lacking in carrying maximum covert information as the number of host image pixels and covert image pixels has the ratio 8:1. In our proposed scheme robust and imperceptibility feature is injected using insignificant pixel value divergence of host and a high capacity covert image. We have proposed frequency entropy method that compares frequencies of covert image and host image in FFT (Fast Fourier Transform) domain. The eminent rate of frequency ETM (Entropy Threshold Match) leads to good image quality and information carrying capability. Moreover, our proposed technique also encrypts the secret image in frequency domain with multi flipped permutated random key vector that provides robustness. Therefore, experiments exhibit that this scheme has improved signal to noise ratio and BPP (bits per pixel) in contrast to existing schemes.

«Многовекторная дипломатия» Ж. Ширака (1995–2007 годы)

«Многовекторная дипломатия» Ж. Ширака (1995–2007 годы)

Effect of Hanoi’s multi-vector diplomacy

Effect of Hanoi’s multi-vector diplomacy

Optimal Region growing and Multi-kernel SVM for fault detection in Electrical Equipments using Infrared Thermography Images

Infrared thermography (IRT) has played an essential part in observing and examining thermal defects of electrical equipment without ending, which has vital enormity for the dependability of electrical recorded. This paper dissected the electrical parts are faulted or non-faulted with the help of segmentation and classification model. The features are calculated from the input thermal images and regions of interest (ROI) is segmented by utilising optimal region growing (ORG) technique and faults are classified using multi kernel support vector machine (MKSVM). In the tests, the classification performances from different input features are assessed. For enhancing the performance of the segmentation investigation optimisation procedure that is whale optimisation (WO) is used. Before classifying, the extracted electrical components are fused by using feature level fusion (FLF) procedure to fused vector in all images. These multi kernel classification performance indices, including sensitivity, specificity and accuracy are utilised to recognise the most appropriate input feature and the best arrangement of classifiers. The performance of SVM is contrasted with a neural network. The correlation comes about demonstrating that our technique can accomplish a superior performance with accuracy at 98.21%.

Shunt Active Power Filter Based on Proportional Integral and Multi Vector Resonant Controllers for Compensating Nonlinear Loads

The current tracking control strategy determines the compensation performance of shunt active power filter (SAPF). Due to inadequate compensation of the main harmonic by traditional proportional integral (PI) control, a control algorithm based on PI and multi vector resonant (VR) controllers is proposed to control SAPF. The mathematical model of SAPF is built, and basic principle of VR controller is introduced. Under the synchronous reference frame, the proposed control method based on pole zero cancellation is designed, which narrows the order of the control system and improves the system dynamic response and the control accuracy. Then the feasibility of the method is demonstrated by analyzing the closed loop frequency characteristics of the system. Finally, the simulation and experimental results are carried out to verify the performance of the proposed method.

The Inverse of a Multivector: Beyond the Threshold $$\varvec{p+q=5}$$ p + q = 5

The algorithm of finding an inverse multivector (MV) numerically and symbolically is of paramount importance in the applied Clifford geometric algebra (GA) $$ Cl _{p,q}$$ . The first general MV inversion algorithm was based on matrix representation of MV. The complexity of calculations and the size of the answer in a symbolic form grow exponentially with the dimension $$n=p+q$$ . The breakthrough occurred when Lundholm and then Dadbeh found compact inverse formulas up to dimension $$n\le 5$$ . The formulas were constructed in a form of Clifford product of the initial MV and carefully chosen grade-negation counterparts. In this report we show that the grade-negated self-product method can be extended beyond the threshold $$n=5$$ if, in addition, properly constructed linear combinations of such MV products are used. In particular, we present compact explicit MV inverse formulas for algebras of vector space of dimension $$n=6$$ and show that they embrace all lower dimensional cases as well. For readers convenience, we have also given various MV formulas in a form of grade negations when $$n\le 5$$ .

Some results on multi vector space

In the present paper, a notion of M-basis and multi dimension of a multi vector space is introduced and some of its properties are studied.

A new concept for implant-borne dental rehabilitation; how to overcome the biological weak-spot of conventional dental implants?

BackgroundEvery endosseous dental implant is dependent on an adequate amount and quality of peri-implant hard and soft tissues and their fully functional interaction. The dental implant could fail in cases of insufficient bone and soft tissues or due to a violation of the soft to hard tissues to implant shoulder interface with arising of a secondary bone loss.MethodTo overcome this biological weak-spot, we designed a new implant that allows for multi vector endosseous anchorage around the individual underlying bone, which has to be scanned by computed tomography (CT) or Cone beam CT (CBCT) technique to allow for planning the implant. We developed a workflow to digitally engineer this customized implant made up of two planning steps. First, the implant posts are designed by prosthodontic-driven backward planning, and a wireframe-style framework is designed on the individual bony surface of the recipient site. Next, the two pieces are digitally fused and manufactured as a single piece implant using the SLM technique (selective laser melting) and titanium-alloy-powder.ResultsPreoperative FEM-stress-test of the individual implant is possible before it is inserted sterile in an out-patient procedure.ConclusionUnlike any other historical or current dental implant protocol, our newly developed “individual patient solutions dental” follows the principle of a fully functional and rigid osteosynthesis technology and offers a quick solution for an implant-borne dental rehabilitation in difficult conditions of soft and hard tissues.