Modified ascent sequences, initially defined as the bijective images of ascent sequences under a certain hat map, have also been characterized as Cayley permutations where each entry is a leftmost copy if and only if it is an ascent top. These sequences play a significant role in the study of Fishburn structures. In this paper, we investigate (primitive) modified ascent sequences avoiding a pattern of length 4 by combining combinatorial and algebraic techniques, including the application of the kernel method. Our results confirm several conjectures posed by Cerbai.

In 1959 the Libraries Committee of the African Studies Association undertook a survey of holdings of Africana in American Theological libraries. The official approval of both the American Theological Library Association and the Catholic Library Association was received and inquiries were sent to a selected group of libraries in each Association. The main purpose was to ascertain the location of significant collections of printed material and to uncover, if possible, unknown or unrecorded manuscripts.

In discussing these three papers as they relate to history, it is an essential starting point to realize that the discipline of history is changing and has changed considerably in the last quarter century. History began as an account of the great deeds of our own ancestors, a record of the past that was essentially a backward extension of our own group personality. It long ago outgrew its concern with our tribal past and came to be concerned with the past of other peoples who share our Western culture. More recently, historians have become increasingly concerned with the past of other cultures as well. Some remnants of the older historical tradition are still around, but broadly speaking history now can be defined as the study of change in human society.

With this shifting focus inside the discipline itself, some of the barriers that used to surround history have also begun to disappear. One of these barriers was a distinction between history and pre-history, made according to the kind of evidence that each used. Historians worked with documentary evidence, leaving the pre-historians to worry with the kind of problem that could be solved only through the combined use of archaeology, oral tradition, linguistic evidence, and the like. In African history no such distinction is possible, and it is now generally abandoned. Documentary evidence about the history of Africa south of the Sahara begins about the ninth century, but it has to be used alongside non-documentary evidence. Documentary evidence, used by itself, only begins to tell the whole story when we come to the twentieth century, and even here it overlaps with the oral evidence of people still alive. African history is thus dominantly a history based on mixed data. The old line between history and pre-history is no longer useful, and theJournal of African History recognized this fact when, for convenience, it set a new division between history and pre-history at the beginning of the Iron Age — a date which will, of course, be somewhat different for different parts of Africa.

This paper explores the impact of handle silicon substrate resistivity on substrate noise coupling and its influence on the spectral purity of voltage-controlled oscillators (VCOs). Three VCOs were designed using the 28 nm fully depleted silicon-on-insulator (FD-SOI) technology and fabricated on process-of-reference wafer featuring a handle Si substrate resistivity value of 10 Ω.cm and also on high-resistivity (HR) Si handle wafer of 1 kΩ.cm. The output spectrum of the VCOs was measured under two conditions: with and without a 0 dBm noise signal injected into the substrate. The results demonstrate that passivated HR substrates achieve more than 26 dB reduction in parasitic spurs induced by substrate noise. To the best of the authors’ knowledge, this work presents the first fabrication and measurement of VCOs on HR substrates in FD-SOI technology, highlighting their effectiveness in mitigating substrate noise coupling.

Answering a question of Kaye, we show that the compositional truth theory with the full collection scheme is conservative over Peano Arithmetic. We demonstrate it by showing that countable models of compositional truth which satisfy the internal induction or collection axioms can be end-extended to models of the respective theory.

It is conjectured that for any fixed relatively prime positive integers a,b and c all greater than 1 there is at most one solution to the equation $a^x+b^y=c^z$ in positive integers x, y and z, except for specific cases. We develop the methods in our previous work which rely on a variety from Baker’s theory and thoroughly study the conjecture for cases where c is small relative to a or b. Using restrictions derived from the hypothesis that there is more than one solution to the equation, we obtain a number of finiteness results on the conjecture. In particular, we find some, presumably infinitely many, new values of c with the property that for each such c the conjecture holds true except for only finitely many pairs of a and b. Most importantly we prove that if $c=13$ then the equation has at most one solution, except for $(a,b)=(3,10)$ or (10,3) each of which gives exactly two solutions. Further, our study with the help of the Schmidt Subspace Theorem among others more, brings strong contributions to the study of Pillai’s type Diophantine equations, notably a general and satisfactory result on a well-known conjecture of M. Bennett on the equation $a^x-b^y=c$ for any fixed positive integers a,b and c with both a and b greater than 1. Some conditional results are presented under the abc-conjecture as well.

Let $\Gamma $ be a compact Polish group of finite topological dimension. For a countably infinite subset $S\subseteq \Gamma $, a domatic $\aleph _0$-partition (for its Schreier graph on $\Gamma $) is a partial function $f:\Gamma \rightharpoonup \mathbb {N}$ such that for every $x\in \Gamma $, one has $f[S\cdot x]=\mathbb {N}$. We show that a continuous domatic $\aleph _0$-partition exists, if and only if a Baire measurable domatic $\aleph _0$-partition exists, if and only if the topological closure of S is uncountable. A Haar measurable domatic $\aleph _0$-partition exists for all choices of S. We also investigate domatic partitions in the general descriptive graph combinatorial setting.

When one contemplates the remarkable expansion in research interest in African phenomena among social scientists on both sides of the Atlantic, the need for an up-to-date inventory of completed, continuing and projected research becomes increasingly apparent. Field research is costly; knowledge should be cumulative; reproduction ought to be systematic; and effective rapport with the human actors concerned should be scrupulously preserved. These and many other considerations dictate closer liaison among scholars everywhere in the organization and planning of future research on African subjects.

The purpose of this report is to provide a brief analytical survey of the character of research on Africa recently completed, or currently being pursued, by social scientists associated with European centers. There is, of course, a certain arbitrariness in focusing upon the state of research in European centers only, particularly in view of the very close organizational links between metropolitan institutions and associated research centers and institutes in the African territories. Moreover, as an increasingly greater proportion of the total research activity is being carried on by agencies established in Africa, a survey of the European centers provides us with only a partial picture of the overall dimensions of research sponsored and supported by the European countries concerned. In this report, however, space considerations unfortunately dictate this narrower focus upon the European side only.