Cardinal invariants for $\kappa$-box products: weight, density character and Suslin number

2016 ◽  
Vol 516 ◽  
pp. 1-41 ◽  
Author(s):  
W. W. Comfort ◽  
Ivan S. Gotchev
Keyword(s):  
Density Character ◽  
Cardinal Invariants ◽  
Weight Density

scholarly journals Quasicontinuous functions and the topology of uniform convergence on compacta

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 911-917
Author(s):  
Lubica Holá ◽  
Dusan Holý
Keyword(s):  
Topological Space ◽  
Uniform Convergence ◽  
Continuous Functions ◽  
Hausdorff Topological Space ◽  
Cardinal Invariants ◽  
Weight Density ◽  
Quasicontinuous Functions

Let X be a Hausdorff topological space, Q(X,R) be the space of all quasicontinuous functions on X with values in R and ?UC be the topology of uniform convergence on compacta. If X is hemicompact, then (Q(X,R), ?UC) is metrizable and thus many cardinal invariants, including weight, density and cellularity coincide on (Q(X,R), ?UC). We find further conditions on X under which these cardinal invariants coincide on (Q(X,R), ?UC) as well as characterizations of some cardinal invariants of (Q(X,R), ?UC). It is known that the weight of continuous functions (C(R,R), ?UC) is ?0. We will show that the weight of (Q(R,R), ?UC) is 2c.

Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle

2005 ◽  
Vol 11 (4) ◽  
pp. 517-525
Author(s):  
Juris Steprāns
Keyword(s):  
Harmonic Analysis ◽  
Set Theory ◽  
Harmonic Functions ◽  
Maximal Functions ◽  
Pigeonhole Principle ◽  
Cardinal Invariants ◽  
Geometric Objects

AbstractIt is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.

CARDINAL INVARIANTS AND SETS OF REALS

1995 ◽  
Vol 21 (1) ◽  
pp. 78
Author(s):  
Bartoszyński
Keyword(s):  
Cardinal Invariants

scholarly journals Improving the Smoothed Complexity of FLIP for Max Cut Problems

2021 ◽  
Vol 17 (3) ◽  
pp. 1-38
Author(s):  
Ali Bibak ◽  
Charles Carlson ◽  
Karthekeyan Chandrasekaran
Keyword(s):  
General Framework ◽  
Edge Weight ◽  
Complete Graphs ◽  
Worst Case ◽  
Weight Density ◽  
Complete Problems ◽  
Substantial Progress ◽  
Run Time ◽  
Optimum Solution ◽  
Arbitrary Graphs

Finding locally optimal solutions for MAX-CUT and MAX- k -CUT are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP method. Even though FLIP requires exponential time in worst-case instances, it tends to terminate quickly in practical instances. To explain this discrepancy, the run-time of FLIP has been studied in the smoothed complexity framework. Etscheid and Röglin (ACM Transactions on Algorithms, 2017) showed that the smoothed complexity of FLIP for max-cut in arbitrary graphs is quasi-polynomial. Angel, Bubeck, Peres, and Wei (STOC, 2017) showed that the smoothed complexity of FLIP for max-cut in complete graphs is ( O Φ 5 n 15.1 ), where Φ is an upper bound on the random edge-weight density and Φ is the number of vertices in the input graph. While Angel, Bubeck, Peres, and Wei’s result showed the first polynomial smoothed complexity, they also conjectured that their run-time bound is far from optimal. In this work, we make substantial progress toward improving the run-time bound. We prove that the smoothed complexity of FLIP for max-cut in complete graphs is O (Φ n 7.83 ). Our results are based on a carefully chosen matrix whose rank captures the run-time of the method along with improved rank bounds for this matrix and an improved union bound based on this matrix. In addition, our techniques provide a general framework for analyzing FLIP in the smoothed framework. We illustrate this general framework by showing that the smoothed complexity of FLIP for MAX-3-CUT in complete graphs is polynomial and for MAX - k - CUT in arbitrary graphs is quasi-polynomial. We believe that our techniques should also be of interest toward showing smoothed polynomial complexity of FLIP for MAX - k - CUT in complete graphs for larger constants k .

Converse dual cardinals

2006 ◽  
Vol 71 (1) ◽  
pp. 22-34 ◽  
Author(s):  
Jörg Brendle ◽  
Shuguo Zhang
Keyword(s):  
Natural Numbers ◽  
Cardinal Invariants ◽  
The Continuum

AbstractWe investigate the set (ω) of partitions of the natural numbers ordered by ≤* where A ≤* B if by gluing finitely many blocks of A we can get a partition coarser than B. In particular, we determine the values of a number of cardinals which are naturally associated with the structure ((ω), ≥*), in terms of classical cardinal invariants of the continuum.

Cardinal invariants of infinite groups

1990 ◽  
Vol 30 (3) ◽  
pp. 155-170
Author(s):  
Jörg Brendle
Keyword(s):  
Infinite Groups ◽  
Cardinal Invariants

Coumarin Content and Physicochemical Profile of Mikania laevigata Extracts

2004 ◽  
Vol 59 (3-4) ◽  
pp. 197-200 ◽  
Author(s):  
Maique W. Biavatti ◽  
Cesar A. Koerich ◽  
Carlos H. Henck ◽  
Enderson Zucatelli ◽  
Fernanda H. Martineli ◽  
...  
Keyword(s):  
Efficient Method ◽  
Extraction Method ◽  
Dry Weight ◽  
Southern Brazil ◽  
Weight Density ◽  
Ethanol Content ◽  
Mikania Laevigata ◽  
Method Of Extraction

The ‘guaco’ lianous herb Mikania laevigata, which is widespread in Southern Brazil, is traditionally used to treat bronchitis, asthma and cough. This work investigates the influence of the extraction method, solvent:drug ratio, ethanol proportion, harvest season (summer or winter) and solvent heating on the physicochemical profile of the extracts (dry weight, density, pH) and the coumarin (1,2-benzopyrone) content determined by LC. Among the results obtained, it is observed that higher ethanol content increases the amount of coumarin in the extract. Leaves harvested in summer also produce an extract with a high coumarin yield. The most efficient method of extraction is percolation, independent of the solvent used.

Material Behavior of 2D Steel Lattices with Different Unit-Cell Patterns

2021 ◽  
Vol 1046 ◽  
pp. 15-21
Author(s):  
Paiboon Limpitipanich ◽  
Pana Suttakul ◽  
Yuttana Mona ◽  
Thongchai Fongsamootr
Keyword(s):  
Elastic Modulus ◽  
Experimental Studies ◽  
Base Material ◽  
Unit Cell ◽  
Material Behavior ◽  
Closed Form Solutions ◽  
The Past ◽  
Weight Density ◽  
Unit Cells ◽  
Cell Patterns

Over the past years, two-dimensional lattices have attracted the attention of several researchers because they are lightweight compared with their full-solid counterparts, which can be used in various engineering applications. Nevertheless, since lattices are manufactured by reducing the base material, their stiffnesses then become lower. This study presents the weight efficiency of the lattices defined by relations between the elastic modulus and the weight density of the lattices. In this study, the mechanical behavior of 2D lattices is described by the in-plane elastic modulus. Experimental studies on the elastic modulus of the 2D lattices made of steel are performed. Three lattices having different unit cells, including square, body-centered, and triangular unit cells, are considered. The elastic modulus of each lattice is investigated by tensile testing. All specimens of the lattices are made of steel and manufactured by waterjet cutting. The experimental results of the elastic modulus of the lattices with the considered unit-cell patterns are validated with those obtained from finite element simulations. The results obtained in this study are also compared with the closed-form solutions founded in the literature. Moreover, the unit-cell pattern yielding the best elastic modulus for the lattice is discussed through weight efficiency.

Cardinal Invariants of l-Topologies

2004 ◽  
Vol 45 (2) ◽  
pp. 241-247
Author(s):  
N. V. Velichko
Keyword(s):  
Cardinal Invariants

scholarly journals Weight, Density and Space in the Norwegian Reindeer Crisis–Notes Towards a Critique

2014 ◽  
Vol 2 (2) ◽  
pp. 153-183 ◽  
Author(s):  
Hugo Reinert
Keyword(s):  
Urban Spaces ◽  
Weight Functions ◽  
Assessment Practices ◽  
Current Management ◽  
Northern Norway ◽  
Weight Density ◽  
Quantitative Metrics ◽  
Reindeer Population ◽  
Core Issues

For decades now, the dominant narrative about indigenous reindeer pastoralism in northern Norway has been that there is a crisis of excess: an oversized reindeer population, poorly held in check by poorly governed herders, is overgrazing the tundra, degrading the pasture grounds, spilling over into urban spaces and precipitating moral crises by starving to death “out there,” on the tundra. Set against the background of this ongoing crisis, the present paper focuses on a set of particularly dense conceptual intersections that cluster around the notion of weight , and the manner in which weight functions both as a crisis indicator and a metric for assessment in contemporary Norwegian pastoral governance. Tracing the work and structure of the weight concept as applied to reindeer–against a dominant government narrative that parses numerical indicators as neutral, objective and apolitical–the paper outlines some of the erasures that the weight metric simultaneously carries out and occludes. The aim of the exercise is to specify and critically reframe certain core issues in the current management of Norwegian pastoralism, by problematising the supposedly neutral, scientific operation of quantitative metrics and assessment practices.

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