scholarly journals Determination of the Properties of (p, q)‐Sigmoid Polynomials and the Structure of Their Roots

2020 ◽  
Author(s):  
Jung Yoog Kang
Keyword(s):  
Fixed Points ◽  
Recurrence Formula ◽  
Addition Theorem ◽  
Euler Polynomials ◽  
Self Similarity ◽  
Research Areas ◽  
Symmetric Relations ◽  
Symmetric Property

Nowadays, many mathematicians have great concern about p q -numbers, which are various applications, and have studied these numbers in many different research areas. We know that p q -numbers are different to q -numbers because of the symmetric property. We find the addition theorem, recurrence formula, and p q -derivative about sigmoid polynomials including p q -numbers. Also, we derive the relevant symmetric relations between p q -sigmoid polynomials and p q -Euler polynomials. Moreover, we observe the structures of appreciative roots and fixed points about p q -sigmoid polynomials. By using the fixed points of p q -sigmoid polynomials and Newton’s algorithm, we show self-similarity and conjectures about p q -sigmoid polynomials.

Determination of Total Choline by Liquid Chromatography– Electrospray Ionization–Tandem Mass Spectrometry in Infant Formulas

2012 ◽  
Vol 95 (1) ◽  
pp. 157-162 ◽  
Author(s):  
Shishan Fu ◽  
Baohua Tao ◽  
Shiyun Lai ◽  
Jingshun Zhang ◽  
Ren Yiping
Keyword(s):  
Electrospray Ionization ◽  
Neural Development ◽  
Internal Standard ◽  
Water Soluble ◽  
Infant Formulas ◽  
Research Areas ◽  
Hydrolyzed Protein ◽  
Evaluation Matrix ◽  
Single Laboratory

Abstract Choline is a water-soluble nutrient important for infants' brain and neural development. In infant formulas, choline is one of the important fortified nutrients. A single-laboratory validation study conducted an LC-electrospray ionization-MS/MS to determine total choline in infant formulas. Sample preparation was adopted from AOAC Official MethodSM 999.14, and instrumental running conditions were optimized. The LOQ was 0.2 μg/100 g, which is significant for measuring total choline in infant formulas. Average recoveries for milk-, rice-, soybean-, and hydrolyzed protein-based samples ranged from 86.45 ± 6.04% to 108.98 ± 3.68%, with RSD less than 7%. The repeatability RSD (RSDr) range was 0.24–3.59% in within-day evaluation and 1.16–3.24% in day-to-day evaluation. Matrix effect was also investigated, and can be effectively eliminated by using an internal standard. Therefore, this method has high credibility, and could be used as a routine method of quality control, or for clinical studies and other research areas.

Applicability of the Homotopy Method to the determination of fixed points in chemical kinetics models

2000 ◽  
Vol 109 (1) ◽  
pp. 31-49
Author(s):  
H. Labro ◽  
B. Maheu ◽  
A. Garo
Keyword(s):  
Fixed Points ◽  
Chemical Kinetics ◽  
Homotopy Method ◽  
Kinetics Models

Determination of fixed points and shift cycles for nearest neighbor cellular automata

1992 ◽  
Vol 66 (5-6) ◽  
pp. 1397-1414 ◽  
Author(s):  
Burton Voorhees1
Keyword(s):  
Cellular Automata ◽  
Fixed Points ◽  
Nearest Neighbor

The nature of discrete second-order self-similarity

2003 ◽  
Vol 35 (02) ◽  
pp. 395-416 ◽  
Author(s):  
A. Gefferth ◽  
D. Veitch ◽  
I. Maricza ◽  
S. Molnár ◽  
I. Ruzsa
Keyword(s):  
Fixed Points ◽  
Long Range ◽  
Power Laws ◽  
Complete Classification ◽  
Second Order ◽  
General Definition ◽  
Long Range Dependence ◽  
Self Similarity ◽  
New Treatment ◽  
Definition Of

A new treatment of second-order self-similarity and asymptotic self-similarity for stationary discrete time series is given, based on the fixed points of a renormalisation operator with normalisation factors which are not assumed to be power laws. A complete classification of fixed points is provided, consisting of the fractional noise and one other class. A convenient variance time function approach to process characterisation is used to exhibit large explicit families of processes asymptotic to particular fixed points. A natural, general definition of discrete long-range dependence is provided and contrasted with common alternatives. The closely related discrete form of regular variation is defined, its main properties given, and its connection to discrete self-similarity explained. Folkloric results on long-range dependence are proved or disproved rigorously.

scholarly journals Some Identities on the Generalizedq-Bernoulli,q-Euler, andq-Genocchi Polynomials

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Daeyeoul Kim ◽  
Burak Kurt ◽  
Veli Kurt
Keyword(s):  
Recurrence Relations ◽  
Analogous Result ◽  
Bernoulli Polynomials ◽  
Addition Theorem ◽  
Euler Polynomials ◽  
Genocchi Polynomials

Mahmudov (2012, 2013) introduced and investigated someq-extensions of theq-Bernoulli polynomialsℬn,qαx,yof orderα, theq-Euler polynomialsℰn,qαx,yof orderα, and theq-Genocchi polynomials𝒢n,qαx,yof orderα. In this paper, we give some identities forℬn,qαx,y,𝒢n,qαx,y, andℰn,qαx,yand the recurrence relations between these polynomials. This is an analogous result to theq-extension of the Srivastava-Pintér addition theorem in Mahmudov (2013).

Grasp Configurations Optimization of Dexterous Robotic Hand Based on Haptic Exploration Information

2017 ◽  
Vol 14 (04) ◽  
pp. 1750013 ◽  
Author(s):  
Haiwei Gu ◽  
Yuanfei Zhang ◽  
Shaowei Fan ◽  
Minghe Jin ◽  
Hong Liu
Keyword(s):  
Planning Process ◽  
Optimization Method ◽  
Robot Kinematics ◽  
Robotic Hand ◽  
Grasp Planning ◽  
Research Areas ◽  
Haptic Exploration ◽  
Robot Configurations ◽  
Grasp Quality

Haptic exploration and grasp planning by dexterous robot hand are usually two independent research areas. In this paper, the determination of optimal grasp configurations after haptic exploration of unknown objects is discussed. The haptic exploration information is used to select initial grasp points and the corresponding robot configurations, which greatly improve the efficiency of grasp planning process. The feasible searching regions on the object are obtained under the constrains of manipulability and robot kinematics. Then, the optimization method based on KNN search is applied to find the optimal grasp positions in feasible searching regions. The selected optimal grasp points set can achieve high grasp quality under the constrains of robot kinematics and manipulability. The optimization method combines multiple grasp quality metrics, which is fast and feasible in optimal grasp points searching. Experiments validate the feasibility and effectivity of the proposed method.

scholarly journals METHODS OF AUTOMATIC DETERMINATION OF THE POSITION OF A MOVING PLATFORM IN SPACE

2019 ◽  
pp. 71-78
Author(s):  
Illia Fіlіmonov ◽  
◽  
Anatoly Revko ◽  
Igor Lysenko ◽  
◽  
...  
Keyword(s):  
General Information ◽  
Mathematical Representation ◽  
Automatic Determination ◽  
Target Setting ◽  
Moving Platforms ◽  
Research Areas ◽  
Localization Algorithms ◽  
Localization And Mapping ◽  
Moving Platform

Urgency of the research. The existence of the need to improve the accuracy of research areas, including in hard-toreach areas, updates the direction of finding new ways of automatic localization for the task of the robot about collecting the information surrounding it for its own localization and building the environment map. Target setting. Existing methods for determining the location of a moving platform in space have a significant error, which is unacceptable for use in devices designed to operate without human intervention. Actual scientific researches and issues analysis. Research trends show satisfactory results of the introduction of new algorithms based on neural networks, but most of the solutions are designed for large moving platforms, while for small platforms, such as UAVs, solutions are not enough. Uninvestigated parts of general matters defining. Works on the automatic determination of the location of a moving platform often demonstrate the results of experiments that were performed in laboratory conditions. The question arises: how the system will behave when tested in real conditions? The research objective. It is supposed to implement a system of automatic movement of the platform based on modern hardware and localization algorithms. The statement of basic materials. Considered general information for methods of localization and mapping of SLAM, the general algorithm for the operation of methods of SLAM and their mathematical representation are presented. Sensors, that are used in localization tasks, are described and two main SLAM methods with a detailed description are presented. The results of the simulation of the ORB-SLAM2 method were presented. Conclusions. The methods for localizing a moving platform in space and algorithm for the operation of the SLAM methods were reviewed in this paper. The features of SLAM methods and their development prospects are presented.

scholarly journals Some identities and recurrence relations on the two variables Bernoulli, Euler and Genocchi polynomials

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1757-1765
Author(s):  
Veli Kurt ◽  
Burak Kurt
Keyword(s):  
Recurrence Relation ◽  
Recurrence Relations ◽  
Bernoulli Polynomials ◽  
Addition Theorem ◽  
Euler Polynomials ◽  
Genocchi Polynomials

Mahmudov in ([16], [17], [18]) introduced and investigated some q-extensions of the q-Bernoulli polynomials B(?)n,q (x,y) of order ?, the q-Euler polynomials ?(?)n,q (x,y) of order ? and the q-Genocchi polynomials G(?)n,q (x,y) of order ?. In this article, we give some identities for the q-Bernoulli polynomials, q-Euler polynomials and q-Genocchi polynomials and the recurrence relation between these polynomials. We give a different form of the analogue of the Srivastava-Pint?r addition theorem.

The nature of discrete second-order self-similarity

2003 ◽  
Vol 35 (2) ◽  
pp. 395-416 ◽  
Author(s):  
A. Gefferth ◽  
D. Veitch ◽  
I. Maricza ◽  
S. Molnár ◽  
I. Ruzsa
Keyword(s):  
Fixed Points ◽  
Long Range ◽  
Power Laws ◽  
Complete Classification ◽  
Second Order ◽  
General Definition ◽  
Long Range Dependence ◽  
Self Similarity ◽  
New Treatment ◽  
Definition Of

A new treatment of second-order self-similarity and asymptotic self-similarity for stationary discrete time series is given, based on the fixed points of a renormalisation operator with normalisation factors which are not assumed to be power laws. A complete classification of fixed points is provided, consisting of the fractional noise and one other class. A convenient variance time function approach to process characterisation is used to exhibit large explicit families of processes asymptotic to particular fixed points. A natural, general definition of discrete long-range dependence is provided and contrasted with common alternatives. The closely related discrete form of regular variation is defined, its main properties given, and its connection to discrete self-similarity explained. Folkloric results on long-range dependence are proved or disproved rigorously.

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