Abstract:
High school physics teachers often turn to various resources, including the Internet, as they search for engaging physics activities for their students. An important question, especially for new physics teachers, concerns the safety of these activities. Have safety issues been adequately addressed within these activities? The purpose of this article is to emphasize potential safety issues involving high school physics projects as well as to provide a checklist for physics teachers to use as they evaluate activities. If the activity is deemed to contain safety issues, physics teachers are encouraged to attempt to modify the activity to make it safe. If the activity cannot be modified for safety purposes, then it is recommended that the physics teacher search for a different activity. The intention of this article is to provide high school physics teachers with safety information that can be used in preparing safe, inquiry-based, hands-on, engaging and topic-appropriate physics activities for their students.

Abstract:
Expander graphs are widely used in communication problems and construction of error correcting codes. In such graphs, information gets through very quickly. Typically, it is not true for social or biological networks, though we may find a partition of the vertices such that the induced subgraphs on them and the bipartite subgraphs between any pair of them exhibit regular behavior of information flow within or between the vertex subsets. Implications between spectral and regularity properties are discussed.

Abstract:
Il contributo presenta un aggiornamento delle informazioni disponibili sulle sculture provenienti dall’anfiteatro di Verona e sull’arredo interno al monumento, in seguito al recupero o alla rilettura di documentazione; sono poi riesaminate le testimonianze relative ai giochi che vi si svolsero. The paper gives an updating of the available information about the sculptures from the Roman Amphitheater in Verona and about the internal furniture of the monument, after the finding or a new reading of old documents; then the historical data related to the games in the Veronese Arena are re-examined.

Abstract:
Si propone un censimento delle attestazioni di decorazione in bronzo per carri in Italia settentrionale, limitando la ricerca agli elementi figurati. L’indagine, per quanto presumibilmente non esaustiva, ha condotto a un considerevole aumento delle testimonianze note (ora una cinquantina), consentendo alcune osservazioni su botteghe di produzione, proprietari, iconografia, cronologia. A list of the bronze decoration (only figural) for roman chariots in Northern Italy has been collected. The query, even though probably non complete, produced an outstanding increase of the known objects (now about fifty), allowing some remarks about workshops, owners, iconography, cronology.

Abstract:
Words reecho their competence in picture making,When visual space sine qua non to be filled by captivating language floating.Colors, shapes and symbols are crystallized by rhyme, rhythm, meter,Silent pictures are...

Abstract:
Expander graphs are widely used in communication problems and construction of error correcting codes. In such graphs, information gets through very quickly. Typically, it is not true for social or biological networks, though we may find a partition of the vertices such that the induced subgraphs on them and the bipartite subgraphs between any pair of them exhibit regular behavior of information flow within or between the vertex subsets. Implications between spectral and regularity properties are discussed. 1. Introduction We want to go beyond the expander graphs that—for four decades—have played an important role in communication networks; for a summary, see for example, Chung [1] and Hoory et al. [2]. Roughly speaking, the expansion property means that each subset of the graph’s vertices has “many” neighbors (combinatorial view), and hence, information gets through such a graph very “quickly” (probabilistic view). We will not give exact definitions of an expander here as those contain many parameters which are not used later. We rather refer to the spectral and random walk characterization of such graphs, as discussed, among others by Alon [3] and Meil？ and Shi [4]. The general framework of an edge-weighted graph will be used. Expanders have a spectral gap bounded away from zero, where—for a connected graph—this gap is defined as the minimum distance between the normalized Laplacian spectrum (apart from the trivial zero eigenvalue) and the endpoints of the interval, the possible range of the spectrum. The larger is the spectral gap, the more our graph resembles a random graph and exhibits some quasirandom properties, for example, the edge densities within any subset and between any two subsets of its vertices do not differ too much of what is expected, see the Expander Mixing Lemma 2.2 of Section 2. Quasirandom properties and spectral gap of random graphs with given expected degrees are discussed in Chung and Graham [5] and Coja-Oghlan and Lanka [6]. However, the spectral gap appears not at the ends of the normalized Laplacian spectrum in case of generalized random or generalized quasirandom graphs that, in the presence of underlying clusters, have eigenvalues (including the zero) separated from 1, while the bulk of the spectrum is located around 1, see for example, [7]. These structures are usual in social or biological networks having clusters of vertices (that belong to social groups or similarly functioning enzymes) such that the edge density within the clusters and between any pair of the clusters is homogeneous. Such a structure is theoretically

Abstract:
The role of the normalized modularity matrix in finding homogeneous cuts will be presented. We also discuss the testability of the structural eigenvalues and that of the subspace spanned by the corresponding eigenvectors of this matrix. In the presence of a spectral gap between the k-1 largest absolute value eigenvalues and the remainder of the spectrum, this in turn implies the testability of the sum of the inner variances of the k clusters that are obtained by applying the k-means algorithm for the appropriately chosen vertex representatives.

Abstract:
The $k$-way discrepancy $\disc_k (\C)$ of a rectangular array $\C$ of nonnegative entries is the minimum of the maxima of the within- and between-cluster discrepancies that can be obtained by simultaneous $k$-clusterings (proper partitions) of its rows and columns. In the main theorem, irrespective of the size of $\C$, we give the following estimate for the $k$th largest non-trivial singular value of the normalized table: $s_k \le 9\disc_{k } (\C ) (k+2 -9k\ln \disc_{k } (\C ))$, provided $\disc_{k } (\C ) <1$ and $k\le \rk (\C )$. This statement is the converse of Theorem 7 of Bolla \cite{Bolla14}, and the proof uses some lemmas and ideas of Butler \cite{Butler}, where only the $k=1$ case is treated, in which case our upper bound is the tighter. The result naturally extends to the singular values of the normalized adjacency matrix of a weighted undirected or directed graph.

Abstract:
We investigate relations between spectral properties, multiway discrepancies, and degree distribution of generalized random and quasirandom graphs. These properties can be regarded as generalized quasirandom properties, since equivalences between them can also be proved for deterministic graph sequences, irrespective of stochastic models. However, we will distinguish between $O (\sqrt{n})$ and $o (\sqrt{n})$ in some implications, and therefore the statements for the normalized modularity eignvalues and discrepancy (which are equivalent) imply the stronger statements for the adjacency spectrum, vertex-degrees, and graph convergence only under some additional conditions.

Abstract:
Expander graphs are widely used in communication problems and construction of error correcting codes. In such graphs, information gets through very quickly. Typically, it is not true for social or biological networks, though we may find a partition of the vertices such that the induced subgraphs on them and the bipartite subgraphs between any pair of them exhibit regular behavior of information flow within or between the subsets. Implications between spectral and regularity properties are discussed.