scholarly journals A New Approach for Examining $q$-Steiner Systems

10.37236/7106 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Tuvi Etzion
Keyword(s):  
Necessary Conditions ◽  
Infinite Family ◽  
Steiner System ◽  
Uniform Structure ◽  
Steiner Systems ◽  
Fano Plane ◽  
New Approach ◽  
New Family ◽  
New Type ◽  
Existence Question

One of the most intriguing problems in $q$-analogs of designs and codes is the existence question of an infinite family of $q$-analog of Steiner systems (spreads not included) in general, and the existence question for the $q$-analog of the Fano plane in particular.We exhibit a completely new method to attack this problem. In the process we define a new family of designs whose existence is implied by the existence of $q$-Steiner systems, but could exist even if the related $q$-Steiner systems do not exist.The method is based on a possible system obtained by puncturing all the subspaces of the $q$-Steiner system several times. We define  the punctured system as a new type of design and enumerate the number of subspaces of various types that it might have. It will be evident that its existence does not imply the existence of the related $q$-Steiner system. On the other hand, this type of design demonstrates how close can we get to the related $q$-Steiner system.Necessary conditions for the existence of such designs are presented. These necessary conditions will be also necessary conditions for the existence of the related $q$-Steiner system. Trivial and nontrivial direct constructions and a nontrivial recursive construction for such designs are given. Some of the designs have a symmetric structure, which is uniform in the dimensions of the existing subspaces in the system. Most constructions are based on this uniform structure of the design or its punctured designs.

scholarly journals Residual $q$-Fano Planes and Related Structures

10.37236/7107 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Tuvi Etzion ◽  
Niv Hooker
Keyword(s):  
Block Design ◽  
Infinite Family ◽  
Steiner System ◽  
Interesting Case ◽  
Common Belief ◽  
Steiner Systems ◽  
Fano Plane ◽  
Open Problems ◽  
One Step ◽  
Existence Question

One of the most intriguing problems for $q$-analogs of designs, is the existence question of an infinite family of $q$-Steiner systems that are not spreads. In particular the most interesting case is the existence question for the $q$-analog of the Fano plane, known also as the $q$-Fano plane. These questions are in the front line of open problems in block design. There was a common belief and a conjecture that such structures do not exist. Only recently, $q$-Steiner systems were found for one set of parameters. In this paper, a definition for the $q$-analog of the residual design is presented. This new definition is different from previous known definition, but its properties reflect better the $q$-analog properties. The existence of a design with the parameters of the residual $q$-Steiner system in general and the residual $q$-Fano plane in particular are examined. We construct different residual $q$-Fano planes for all $q$, where $q$ is a prime power. The constructed structure is just one step from a construction of a $q$-Fano plane.

scholarly journals An Intrinsic Characterization of Five Points in a CAT(0) Space

2020 ◽  
Vol 8 (1) ◽  
pp. 114-165
Author(s):  
Tetsu Toyoda
Keyword(s):  
Metric Space ◽  
Isometric Embedding ◽  
Metric Spaces ◽  
Necessary Conditions ◽  
New Approach ◽  
Intrinsic Characterization ◽  
New Family

AbstractGromov (2001) and Sturm (2003) proved that any four points in a CAT(0) space satisfy a certain family of inequalities. We call those inequalities the ⊠-inequalities, following the notation used by Gromov. In this paper, we prove that a metric space X containing at most five points admits an isometric embedding into a CAT(0) space if and only if any four points in X satisfy the ⊠-inequalities. To prove this, we introduce a new family of necessary conditions for a metric space to admit an isometric embedding into a CAT(0) space by modifying and generalizing Gromov’s cycle conditions. Furthermore, we prove that if a metric space satisfies all those necessary conditions, then it admits an isometric embedding into a CAT(0) space. This work presents a new approach to characterizing those metric spaces that admit an isometric embedding into a CAT(0) space.

scholarly journals Cryogenic Exfoliation of 2D Stanene Nanosheets for Cancer Theranostics

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Jiang Ouyang ◽  
Ling Zhang ◽  
Leijiao Li ◽  
Wei Chen ◽  
Zhongmin Tang ◽  
...  
Keyword(s):  
Biomedical Applications ◽  
Density Functional ◽  
Biomedical Application ◽  
Density Functional Theory Calculations ◽  
Free Electrons ◽  
Functional Theory ◽  
New Approach ◽  
New Type ◽  
Average Size ◽  
Cancer Theranostics

Abstract Stanene (Sn)-based materials have been extensively applied in industrial production and daily life, but their potential biomedical application remains largely unexplored, which is due to the absence of the appropriate and effective methods for fabricating Sn-based biomaterials. Herein, we explored a new approach combining cryogenic exfoliation and liquid-phase exfoliation to successfully manufacture two-dimensional (2D) Sn nanosheets (SnNSs). The obtained SnNSs exhibited a typical sheet-like structure with an average size of ~ 100 nm and a thickness of ~ 5.1 nm. After PEGylation, the resulting PEGylated SnNSs (SnNSs@PEG) exhibited good stability, superior biocompatibility, and excellent photothermal performance, which could serve as robust photothermal agents for multi-modal imaging (fluorescence/photoacoustic/photothermal imaging)-guided photothermal elimination of cancer. Furthermore, we also used first-principles density functional theory calculations to investigate the photothermal mechanism of SnNSs, revealing that the free electrons in upper and lower layers of SnNSs contribute to the conversion of the photo to thermal. This work not only introduces a new approach to fabricate 2D SnNSs but also establishes the SnNSs-based nanomedicines for photonic cancer theranostics. This new type of SnNSs with great potential in the field of nanomedicines may spur a wave of developing Sn-based biological materials to benefit biomedical applications.

A new approach to the stability analysis of thawing slopes

1980 ◽  
Vol 17 (4) ◽  
pp. 607-612 ◽  
Author(s):  
Luis E. Vallejo
Keyword(s):  
Stability Analysis ◽  
Water Content ◽  
Pore Water ◽  
Active Layer ◽  
Necessary Conditions ◽  
Mass Movements ◽  
New Approach ◽  
Pore Water Pressures ◽  
The Stability ◽  
Excess Pore

A new approach to the stability analysis of thawing slopes at shallow depths, taking into consideration their structure (this being a mixture of hard crumbs of soil and a fluid matrix), is presented. The new approach explains shallow mass movements such as skin flows and tongues of bimodal flows, which usually take place on very low slope inclinations independently of excess pore water pressures or increased water content in the active layer, which are necessary conditions in the methods available to date to explain these movements.

scholarly journals Scientia est potentia

2009 ◽  
pp. 43-60
Author(s):  
Ülo Kaevats
Keyword(s):  
Modern Science ◽  
New Approach ◽  
Natural Laws ◽  
Modern Times ◽  
Natural Objects ◽  
Deductive Method ◽  
New Type ◽  
The Subject ◽  
Understanding Of Science ◽  
Object Of Study

Oma algses mitmetähenduslikkuses on see F. Baconi aforism kõige tihendatum tõdemus, mis tõmbab olemusliku eraldusjoone ühelt poolt antiikse ja keskaegse ning teisalt uusaegse arusaama vahele teadusest ja teadusteadmisest. Artiklis püüab autor anda võimaluste piires tervikpildi uusaja teaduse industriaalselt (tehnoloogiliselt) orienteeritud teadmistüübi tekkimisest. Uusaja teaduse kujunemiseks vajaliku pöörde maailmavaateliste eeldustena tuleb käsitleda: (1) põhimõtteliselt uut subjekti ja objekti käsitust; (2) täiesti uut väärtusruumi, uut teaduse ideoloogiat (ilmalikkus, kriitiline vaim, tõesus ja praktiline kasulikkus); (3) tunnetuslaadi muutust — kontemplatsioonilt interventsioonile, kvaliteedi kirjeldamiselt kvantiteedi uurimisele; (4) looduse käsitlemist Kosmose asemel seaduspäraselt korrastatud objektide “väljana”. Uue tunnetusstiili — empiirilise ja teoreetilise tunnetuse kokkuviimine, hüpoteetilis-deduktiivse metodoloogia kujundamine Galilei poolt, abstraktse ja sünteetilis-tekstilise loomuga spekulatsiooni asendumine uurimisobjekti ehituse, korrapära ja põhjuslikkuse objektiivse analüüsiga, universaalsete loodusseaduste doktriini kujunemine jms—kujunemine konstitueeris uut tüüpi teadmise. Teadmise kui nähtava maailma piltkoopia asemele luuakse teadmine kui loodusobjektide seaduspära analüütiline rekonstruktsioon. See on vormiltmatemaatiline, päritolult eksperimentaalne ning loodusobjektide kontrollimisele ja ümbertegemisele suunatud nn valdamisteadmine.This F. Bacon's aphorism in its original ambiguity is the most condensed belief that draws a distinctive essential line between ancient and medieval understanding of science and scientific knowledge on one hand and modern understanding on the other. The author aims at providing, as far as possible, an integral overview of emerging of the industrially (technologically) orientated type of knowledge of modern times. Ideological/philosophical preconditions of the change necessary for emerging of modern science are: (1) a fundamentally new approach to the subject and object; (2) a completely new system of values, a new ideology of science (secularity, critical spirit, trueness and utilitarianism); (3) a change in manner of cognizance - from contemplation to intervention, from describing quality to studying quantity; (4) treating nature as a naturally organised "field" of objects instead of the Cosmos. Emerging of a new style of cognizance - bringing together of empirical and theoretical cognition, the devise of the hypothetical-deductive method by Galilei, replacement of speculations abstract and synthetic-textual in nature with objective study of the structure, regularity and causality of the object of study, establishment of the doctrine of universal natural laws etc - constituted a new type of knowledge. Knowledge as a copy of the visible world is replaced by knowledge as an analytical reconstruction of the regularity of natural objects. It is so-called dispositive knowledge, morphologically mathematical, originally experimental and aimed at control and alteration of natural objects.

scholarly journals AILU FOR HELMHOLTZ PROBLEMS: A NEW PRECONDITIONER BASED ON THE ANALYTIC PARABOLIC FACTORIZATION

2001 ◽  
Vol 09 (04) ◽  
pp. 1499-1506 ◽  
Author(s):  
MARTIN J. GANDER ◽  
FRÉDÉRIC NATAF
Keyword(s):  
Numerical Experiments ◽  
New Approach ◽  
New Type

We investigate a new type of preconditioner which is based on the analytic factorization of the operator into two parabolic factors. Approximate analytic factorizations lead to new block ILU preconditioners. We analyze the preconditioner at the continuous level where it is possible to optimize its performance. Numerical experiments illustrate the effectiveness of the new approach.

Direct Product of Derived Steiner Systems Using Inversive Planes

1981 ◽  
Vol 33 (6) ◽  
pp. 1365-1369 ◽  
Author(s):  
K. T. Phelps
Keyword(s):  
Direct Product ◽  
Triple System ◽  
Steiner Triple System ◽  
Steiner System ◽  
Steiner Systems

A Steiner system S(t, k, v) is a pair (P, B) where P is a v-set and B is a collection of k-subsets of P (usually called blocks) such that every t-subset of P is contained in exactly one block of B. As is well known, associated with each point x ∈ P is a S(t � 1, k � 1, v � 1) defined on the set Px = P\{x} with blocksB(x) = {b\{x}|x ∈ b and b ∈ B}.The Steiner system (Px, B(x)) is said to be derived from (P, B) and is called (obviously) a derived Steiner (t – 1, k – 1)-system. Very little is known about derived Steiner systems despite much effort (cf. [11]). It is not even known whether every Steiner triple system is derived.Steiner systems are closely connected to equational classes of algebras (see [7]) for certain values of k.

Part Accuracy Management by Topological Mapping of Deviations

2016 ◽  
Vol 859 ◽  
pp. 210-216
Author(s):  
Gabriel Frumuşanu ◽  
Alexandru Epureanu
Keyword(s):  
Geometrical Model ◽  
Synthetic Approach ◽  
Concrete Case ◽  
Topological Map ◽  
New Approach ◽  
Part Geometry ◽  
Real Geometry ◽  
Geometric Deviations ◽  
New Type ◽  
Modern Manufacturing

Despite modern manufacturing processes are characterized by a continuously increasing accuracy, geometric deviations inherently appear on every manufactured part so, for quality-aware companies, it is essential to control and to manage them. This paper introduces a new type of part geometrical model, namely the part topological map, in connection with a new approach in part accuracy management. The part topological map enables a global analytical & synthetic approach of the problems related to tolerancing domain and a generalization of the “part accuracy” concept. The part geometry is seen as a stand-alone ensemble of surfaces dimensionally related, unitary and with its own shape, dimensions and position. The real geometry has also a global, unitary deviation, characterized through deviation features. Each component surface is represented in a particular manner, unrolled, while its deviation features are assessed by using series expansion of the deviations corresponding to a cloud of measured points. A method for effectively realizing the topological map of a part deviation and a numerical exercise to illustrate the method application in a concrete case are also included.

scholarly journals Constructive basis for the development of the extreme zones of Siberia and the Russian arctic

2018 ◽  
Vol 7 (2.13) ◽  
pp. 75
Author(s):  
Tat'yana Sarvut
Keyword(s):  
Structural Changes ◽  
Irreversible Process ◽  
World Ocean ◽  
Weather Conditions ◽  
Russian Arctic ◽  
Protective Measures ◽  
New Approach ◽  
The World ◽  
The Face ◽  
New Type

The paper describes the constructive basis for building and structure designing in the difficult regions of Siberia and the Russian Arctic and development of a new approach to the design of buildings and structures in the Russian Arctic in the face of climate change. Severe climate and weather conditions of the northwestern territories of Russia are rapidly changing due to the global warming. The structural changes in development and construction, following this irreversible process, are highlighted and discussed in relation to the foundations and constructive systems. The paper provides an overview of methods and technological approaches to the extreme zone construction. The application of modern methods of design and construction with the involvement of competent "practitioners" increases the pace of construction and reduces its cost; Architectural and constructive solutions should focus on the developing areas of business and tourism. We suggest the possible protective measures against the transgression of the World Ocean and thawing of the permafrost. The term “special Arctic bases”, denoting the new type of settlements in the Russian Arctic, is introduced. The introduction of constructive solutions and the development of planning solutions for the bases will help to ensure a stable activity in the region.  

Nonlinear Dynamic Response of a Thin Plate in a Fractional Viscoelastic Medium under Internal Resonance 1:1:2

2014 ◽  
Vol 518 ◽  
pp. 60-65 ◽  
Author(s):  
Yury Rossikhin ◽  
Marina Shitikova
Keyword(s):  
Nonlinear Equations ◽  
Time Scales ◽  
Viscoelastic Medium ◽  
Equations Of Motion ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Internal Resonances ◽  
Nonlinear Dynamic Response ◽  
New Approach ◽  
New Type

Dynamic behaviour of a nonlinear plate embedded in a fractional derivative viscoelastic medium and subjected to the conditions of the internal resonances two-to-one has been studied by Rossikhin and Shitikova in [1]. Nonlinear equations, the linear parts of which occur to be coupled, were solved by the method of multiple time scales. A new approach proposed in this paper allows one to uncouple the linear parts of equations of motion of the plate, while the same method, the method of multiple time scales, has been utilized for solving nonlinear equations. The new approach enables one to find a new type of the internal resonanse, i.e., one-to-one-to-two, as well as to solve the problems of vibrations of thin bodies more efficiently.

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