scholarly journals Some identities and reciprocity relationsof unipoly-Dedekind type DC sums

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hye Kyung Kim ◽  
Dae Sik Lee
Keyword(s):  
The Other ◽  
Reciprocity Relation ◽  
Dedekind Sums ◽  
Euler Polynomials ◽  
Euler Function ◽  
Polylogarithm Function

AbstractDedekind type DC sums and their generalizations are defined in terms of Euler functions and their generalization. Recently, Ma et al. (Adv. Differ. Equ. 2021:30 2021) introduced the poly-Dedekind type DC sums by replacing the Euler function appearing in Dedekind sums, and they were shown to satisfy a reciprocity relation. In this paper, we consider two kinds of new generalizations of the poly-Dedekind type DC sums. One is a unipoly-Dedekind type DC sum associated with the type 2 unipoly-Euler functions expressed in the type 2 unipoly-Euler polynomials using the modified polyexponential function, and we study some identities and the reciprocity relation for these unipoly-Dedekind type DC sums. The other is a unipoly-Dedekind sums type DC associated with the poly-Euler functions expressed in the unipoly-Euler polynomials using the polylogarithm function, and we derive some identities and the reciprocity relation for those unipoly-Dedekind type DC sums.

scholarly journals Identities on poly-Dedekind sums

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Hyunseok Lee ◽  
Lee-Chae Jang
Keyword(s):  
Modular Group ◽  
Reciprocity Relation ◽  
Dedekind Sums ◽  
Transformation Behavior ◽  
Dedekind Eta Function ◽  
Bernoulli Function ◽  
Bernoulli Functions

Abstract Dedekind sums occur in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. In 1892, Dedekind showed a reciprocity relation for the Dedekind sums. Apostol generalized Dedekind sums by replacing the first Bernoulli function appearing in them by any Bernoulli functions and derived a reciprocity relation for the generalized Dedekind sums. In this paper, we consider the poly-Dedekind sums obtained from the Dedekind sums by replacing the first Bernoulli function by any type 2 poly-Bernoulli functions of arbitrary indices and prove a reciprocity relation for the poly-Dedekind sums.

scholarly journals Reciprocity of poly-Dedekind-type DC sums involving poly-Euler functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yuankui Ma ◽  
Dae San Kim ◽  
Hyunseok Lee ◽  
Hanyoung Kim ◽  
Taekyun Kim
Keyword(s):  
Modular Group ◽  
Reciprocity Relation ◽  
Dedekind Sums ◽  
Transformation Behavior ◽  
Euler Function ◽  
Dedekind Eta Function ◽  
Reciprocity Relations ◽  
Bernoulli Functions

AbstractThe classical Dedekind sums appear in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. The Dedekind sums and their generalizations are defined in terms of Bernoulli functions and their generalizations, and are shown to satisfy some reciprocity relations. In contrast, Dedekind-type DC (Daehee and Changhee) sums and their generalizations are defined in terms of Euler functions and their generalizations. The purpose of this paper is to introduce the poly-Dedekind-type DC sums, which are obtained from the Dedekind-type DC sums by replacing the Euler function by poly-Euler functions of arbitrary indices, and to show that those sums satisfy, among other things, a reciprocity relation.

scholarly journals Poly-Dedekind sums associated with poly-Bernoulli functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yuankui Ma ◽  
Dae San Kim ◽  
Hyunseok Lee ◽  
Taekyun Kim
Keyword(s):  
Reciprocity Relation ◽  
Dedekind Sums ◽  
Bernoulli Function ◽  
Bernoulli Functions

AbstractApostol considered generalized Dedekind sums by replacing the first Bernoulli function appearing in Dedekind sums by any Bernoulli functions and derived a reciprocity relation for them. Recently, poly-Dedekind sums were introduced by replacing the first Bernoulli function appearing in Dedekind sums by any type 2 poly-Bernoulli functions of arbitrary indices and were shown to satisfy a reciprocity relation. In this paper, we consider other poly-Dedekind sums that are obtained by replacing the first Bernoulli function appearing in Dedekind sums by any poly-Bernoulli functions of arbitrary indices. We derive a reciprocity relation for these poly-Dedekind sums.

The pseudomalachite-ludjibaite-reichenbachite conundrum: OD description

2019 ◽  
Vol 57 (5) ◽  
pp. 571-581
Author(s):  
Emil Makovicky
Keyword(s):  
Crystal Structures ◽  
Current Knowledge ◽  
The Other ◽  
Crystal Chemical ◽  
Layer System ◽  
Coordination Polyhedra

Abstract Crystal structures of the three polymorphs of Cu5(PO4)2(OH)4, namely pseudomalachite, ludjibaite, and reichenbachite, can be described as being composed of rods perpendicular to their crystal-chemical layering. Two different sorts of rods can be defined. Type 1 rods share rows of Cu coordination polyhedra, forming a series of slabs. Slab boundaries and slab interiors represent alternating geometric OD layers of two kinds, with layer symmetries close to P21/m and , which make up two different stacking schemes of geometric OD layers in the structures of ludjibaite and pseudomalachite. Such OD layers, however, are not developed in reichenbachite. Type 2 rods are defined as having columns of PO4 tetrahedra in the corners of the rods. In the Type 2 slabs composed of these rods, geometric Pg OD layers of glide-arrayed tetrahedra alternate with more complex OD layers; in ludjibaite this system of layers is oriented diagonally with respect to the Type 1 OD layer system. Two different OD stackings of Type 2 OD layers form the ludjibaite and reichenbachite structures but not that of pseudomalachite. Thus, ludjibaite might form disordered intergrowths with either of the other two members of the triplet but reichenbachite and pseudomalachite should not form oriented intergrowths. Current knowledge concerning formation of the three polymorphs is considered.

The Effects of Smoking Cessation on Diabetes Mellitus Patients

2020 ◽  
Vol 16 (2) ◽  
pp. 137-142
Author(s):  
Ali Alshahrani
Keyword(s):  
Smoking Cessation ◽  
The Other ◽  
Data Sources ◽  
Controlled Trials ◽  
Effective Management ◽  
Tailored Intervention ◽  
Randomized Controlled ◽  
Increased Risk ◽  
Diabetes Progression

Background: Smoking is an established predictor of type 2 diabetes. However, the link between smoking cessation and diabetes progression remains a subject of scholarly investigation. Objective: The objective of this systematic review is to establish the link between smoking cessation and diabetes. Data Sources: The study utilized conference abstracts and peer-reviewed journals that reported randomized controlled trials smoking cessation interventions for diabetes patients. Results: Results from the review were inconclusive on the link between smoking cessation and diabetes. On one hand, several researchers have confirmed a positive correlation between smoking cessation and decreased risk of diabetes. On the other hand, some researchers have demonstrated that immediate withdrawal of nicotine resulted in increased risk of diabetes; however, this risk reduces with time. Conclusion: The result of this review did not estblish a clear relationship between smoking cessation and diabates. Limitations: Compared to other studies examining the implication of smoking on chronic diseases, this study identified a very small number of trials evaluating the effect of smoking cessation on diabetes. The small number of studies implies that the results may not be suitable for generalization. Implication: Results from the review can help in the development of a tailored intervention for effective management of diabetes in smoking patients.

scholarly journals Development of Type 2 Diabetes Mellitus Phenotyping Framework Using Expert Knowledge and Machine Learning Approach

2016 ◽  
Vol 11 (4) ◽  
pp. 791-799 ◽  
Author(s):  
Rina Kagawa ◽  
Yoshimasa Kawazoe ◽  
Yusuke Ida ◽  
Emiko Shinohara ◽  
Katsuya Tanaka ◽  
...  
Keyword(s):  
Diabetes Mellitus ◽  
Machine Learning ◽  
Type 2 Diabetes ◽  
Type 2 Diabetes Mellitus ◽  
Expert Knowledge ◽  
The Other ◽  
Learning Approach ◽  
Research Subjects ◽  
Machine Learning Approach

Background: Phenotyping is an automated technique that can be used to distinguish patients based on electronic health records. To improve the quality of medical care and advance type 2 diabetes mellitus (T2DM) research, the demand for T2DM phenotyping has been increasing. Some existing phenotyping algorithms are not sufficiently accurate for screening or identifying clinical research subjects. Objective: We propose a practical phenotyping framework using both expert knowledge and a machine learning approach to develop 2 phenotyping algorithms: one is for screening; the other is for identifying research subjects. Methods: We employ expert knowledge as rules to exclude obvious control patients and machine learning to increase accuracy for complicated patients. We developed phenotyping algorithms on the basis of our framework and performed binary classification to determine whether a patient has T2DM. To facilitate development of practical phenotyping algorithms, this study introduces new evaluation metrics: area under the precision-sensitivity curve (AUPS) with a high sensitivity and AUPS with a high positive predictive value. Results: The proposed phenotyping algorithms based on our framework show higher performance than baseline algorithms. Our proposed framework can be used to develop 2 types of phenotyping algorithms depending on the tuning approach: one for screening, the other for identifying research subjects. Conclusions: We develop a novel phenotyping framework that can be easily implemented on the basis of proper evaluation metrics, which are in accordance with users’ objectives. The phenotyping algorithms based on our framework are useful for extraction of T2DM patients in retrospective studies.

Comparing the Arrangements of Governance and Sustainable Development in OECD Countries: Coupled or Decoupled?

2019 ◽  
Vol 34 (1) ◽  
pp. 99-117
Author(s):  
Huh Taewook
Keyword(s):  
Sustainable Development ◽  
Oecd Countries ◽  
The Other ◽  
Type Analysis ◽  
Ideal Types ◽  
Type 3 ◽  
Relationship Of ◽  
The Relationship

This study attempts to analyze to what extent governance and sustainable development (SD) empirically appear compatible in the thirtyfive OECD countries through the fuzzy-set ideal type analysis, and identify which ideal types appear coupled or decoupled, and then reveal which countries belong to the coupled types or to the decoupled types. In short, twenty-two countries (including Sweden (fuzzy score, 0.953), Denmark (0.920), Finland (0.914), Norway (0.911) in Type 1 (G*S, ‘strong G-S coupled countries’); and Turkey (0.906), Greece (0.833), Mexico (0.828) in Type 4 (g*s, ‘lite g-s coupled countries’) are in line with the accepted conventions regarding the compatible relationship between governance and SD. On the other hand, the rest of thirteen countries (including USA (fuzzy score, 0.815), Luxembourg (0.721), Australia (0.660) in Type 2 (G*s, ‘G-s decoupled countries’); and Slovenia (0.728), France (0.644), Czech Rep. (0.625) in Type 3 (g*S, ‘g-S decoupled countries’) may indicate that the relationship of governance and SD is in fact experiencing tensions in the national contexts. These findings are characterized by the substance (of SD) and procedure (of governance) divide. Considering the results, this study focuses on the idea of reflexivity or reflexive capacity.

scholarly journals The Computational Strength of Extensions of Weak König’s Lemma

1998 ◽  
Vol 5 (41) ◽  
Author(s):  
Ulrich Kohlenbach
Keyword(s):  
Natural Number ◽  
Arbitrary Function ◽  
The Other ◽  
Binary Trees ◽  
Subsequent Paper ◽  
Bounded Functions ◽  
The One ◽  
Weak König’S Lemma ◽  
König’S Lemma

The weak König's lemma WKL is of crucial significance in the study of fragments of mathematics which on the one hand are mathematically strong but on the other hand have a low proof-theoretic and computational strength. In addition to the restriction to binary trees (or equivalently bounded trees), WKL<br />is also `weak' in that the tree predicate is quantifier-free. Whereas in general the computational and proof-theoretic strength increases when logically more complex trees are allowed, we show that this is not the case for trees which are<br />given by formulas in a class Phi where we allow an arbitrary function quantifier prefix over bounded functions in front of a Pi^0_1-formula. This results in a schema Phi-WKL.<br />Another way of looking at WKL is via its equivalence to the principle<br /> For all x there exists y<=1 for all z A0(x; y; z) -> there exists f <= lambda x.1 for all x, z A0(x, fx, z);<br />where A0 is a quantifier-free formula (x, y, z are natural number variables). <br /> We generalize this to Phi-formulas as well and allow function quantifiers `there exists g <= s'<br />instead of `there exists y <= 1', where g <= s is defined pointwise. The resulting schema is called Phi-b-AC^0,1.<br />In the absence of functional parameters (so in particular in a second order context), the corresponding versions of Phi-WKL and Phi-b-AC^0,1 turn out to<br />be equivalent to WKL. This changes completely in the presence of functional<br />variables of type 2 where we get proper hierarchies of principles Phi_n-WKL and<br />Phi_n-b-AC^0,1. Variables of type 2 however are necessary for a direct representation<br />of analytical objects and - sometimes - for a faithful representation of<br />such objects at all as we will show in a subsequent paper. By a reduction of<br />Phi-WKL and Phi-b-AC^0,1 to a non-standard axiom F (introduced in a previous paper) and a new elimination result for F relative to various fragment of arithmetic in all finite types, we prove that Phi-WKL and Phi-b-AC^0,1 do<br />neither contribute to the provably recursive functionals of these fragments nor to their proof-theoretic strength. In a subsequent paper we will illustrate the greater mathematical strength of these principles (compared to WKL).

Relational problems are not fully solved by a temporal sequence of statistical learning episodes

1997 ◽  
Vol 20 (1) ◽  
pp. 82-82 ◽  
Author(s):  
A. Vinter ◽  
P. Perruchet
Keyword(s):  
Implicit Learning ◽  
Statistical Learning ◽  
Temporal Sequence ◽  
The Other ◽  
Learning Mechanisms ◽  
Learning Research ◽  
The One

Clark & Thornton's conception finds an echo in implicit learning research, which shows that subjects may perform adaptively in complex structured situations through the use of simple statistical learning mechanisms. However, the authors fail to draw a distinction between, on the one hand, subjects' representations which emerge from type-1 learning mechanisms, and, on the other, their knowledge of the genuine abstract “recoding function” which defines a type-2 problem.

scholarly journals Monoclonal Antibodies That Distinguish Antigenic Variants of Canine Parvovirus

2003 ◽  
Vol 10 (6) ◽  
pp. 1085-1089 ◽  
Author(s):  
Masato Nakamura ◽  
Kazuya Nakamura ◽  
Takayuki Miyazawa ◽  
Yukinobu Tohya ◽  
Masami Mochizuki ◽  
...  
Keyword(s):  
Monoclonal Antibodies ◽  
Antigenic Site ◽  
Canine Parvovirus ◽  
The Other ◽  
Escape Mutants ◽  
Feline Parvovirus ◽  
Resistant Mutants ◽  
Selection Of

ABSTRACT Canine parvovirus (CPV) is classified as a member of the feline parvovirus (FPV) subgroup. CPV isolates are divided into three antigenic types: CPV type 2 (CPV-2), CPV-2a, and CPV-2b. Recently, new antigenic types of CPV were isolated from Vietnamese leopard cats and designated CPV-2c(a) or CPV-2c(b). CPV-2c viruses were distinguished from the other antigenic types of the FPV subgroup by the absence of reactivity with several monoclonal antibodies (MAbs). To characterize the antigenicity of CPV-2c, a panel of MAbs against CPV-2c was generated and epitopes recognized by these MAbs were examined by selection of escape mutants. Four MAbs were established and classified into three groups on the basis of their reactivities: MAbs which recognize CPV-2a, CPV-2b, and CPV-2c (MAbs 2G5 and 20G4); an MAb which reacts with only CPV-2b and CPV-2c(b) (MAb 21C3); and an MAb which recognizes all types of the FPV subgroup viruses (MAb 19D7). The reactivity of MAb 20G4 with CPV-2c was higher than its reactivities with CPV-2a and CPV-2b. These types of specificities of MAbs have not been reported previously. A mapping study by analysis of neutralization-resistant mutants showed that epitopes recognized by MAbs 21C3 and 19D7 belonged to antigenic site A. Substitution of the residues in site B and the other antigenic site influenced the epitope recognized by MAb 2G5. It was suggested that the epitope recognized by MAb 20G4 was related to antigenic site B. These MAbs are expected to be useful for the detection and classification of FPV subgroup isolates.

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