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Start Over Coverage 45-53

1. End-faithful spanning trees of countable graphs with prescribed sets of rays

Creator:
Polat, Norbert
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
math, countable graphs, and prescribed sets of rays
Language:
English
Description:
We prove that a countable connected graph has an end-faithful spanning tree that contains a prescribed set of rays whenever this set is countable, and we show that this solution is, in a certain sense, the best possible. This improves a result of Hahn and Širáň Theorem 1.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Interpolation theorems for a family of spanning subgraphs

Creator:
Zhou, San Ming
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
math, theorems, and subgraphs
Language:
English
Description:
Let $G$ be a graph with order $p$, size $q$ and component number $\omega $. For each $i$ between $p - \omega $ and $q$, let ${\mathcal C}_{i}(G)$ be the family of spanning $i$-edge subgraphs of $G$ with exactly $\omega $ components. For an integer-valued graphical invariant $\varphi $, if $H \rightarrow H^{\prime }$ is an adjacent edge transformation (AET) implies $|\varphi (H) - \varphi (H^{\prime })| \le 1$, then $\varphi $ is said to be continuous with respect to AET. Similarly define the continuity of $\varphi $ with respect to simple edge transformation (SET). Let $M_{j}(\varphi )$ and $m_{j}(\varphi )$ be the invariants defined by $M_{j}(\varphi )(H) = \max _{T \in {\mathcal C}_{j}(H)} \varphi (T)$, $ m_{j}(\varphi )(H) = \min _{T \in {\mathcal C}_{j}(H)} \varphi (T) $. It is proved that both $M_{p - \omega }(\varphi )$ and $m_{p - \omega }(\varphi )$ interpolate over $\mathbf{{\mathcal C}_{i}(G)}$, $ p - \omega \le i \le q$, if $\varphi $ is continuous with respect to AET, and that $M_{j}(\varphi )$ and $m_{j}(\varphi )$ interpolate over $\mathbf{{\mathcal C}_{i}(G)}$, $p - \omega \le j \le i \le q$, if $\varphi $ is continuous with respect to SET. In this way a lot of known interpolation results, including a theorem due to Schuster etc., are generalized.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Morphology and taxonomy of Salvelinema species (Nematoda: Cystidicolidae), swimbladder parasites of Pacific area salmonids

Creator:
Moravec, František and Nagasawa, Kazuya
Format:
print
Type:
model:internalpart and TEXT
Subject:
Salvelinema, swimbladder nematodes, Oncorhynchus, Salvelinus, Japan, and Canada
Language:
English
Description:
The morphology of two Salvelinema Trofimenko, 1962 species, S. salmonicola (Ishii, 1916) and S. walkeri (F.kbaum, 1935), swimbladder nematodes of salmonids, was studied in detail, including scanning electron microscopy (SEM), on the basis of newly collected materials from Oncorhynchus masou, О. mykiss and Salvelinus malma from Japan and from Oncorhynchus ciarki, О. kisulch and O. nerka from North America (Vancouver Island, B.C., Canada and Gulf of Alaska). Both nematode species proved to be morphologically very similar, differing substantially in the numbers and arrangements of egg filaments. Deirids were described for the first time for Salvelinema. Salvelinema iwana (Fujita, 1928), S. amemasu (Fujita, 1939), S. kosugii (Fujita, 1939), S. oncorhynchi (Fujita, 1939) and S. salvelini (Fujita, 1939) (= S. ishii (Fujita, 1941)) were synonymised with S. salmonicola. Comephoronema Layman, 1933 is re-erected as a valid genus related to Salvelinema.
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public

4. On Korovkin type theorem in the space of locally integrable functions

Creator:
Gadjiev, A. D., Efendiyev, R. O., and Ibikli, E.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
linear positive operators, Korovkin type theorem, and weighted $L_p({\mathrm loc})$ spaces
Language:
English
Description:
It is shown that a Korovkin type theorem for a sequence of linear positive operators acting in weighted space $L_{p,w}({\mathrm loc})$ does not hold in all this space and is satisfied only on some subspace.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public