Generalized Euler constants

We define a family {$\gamma(P)$} of generalized Euler constants indexed by finite sets of primes $P$ and study their distribution. These arise from partial sums of reciprocals of integers not divisible by any prime in $P$. An apparent monotonicity is investigated. We also prove that a certain property of these numbers is equivalent to the Riemann Hypothesis.Comment: v2. 13 pages. Minor changes suggested by the referee. To appear in Math. Proc. Cambridge Phil. So

Large-Nc QCD, Harmonic Sums and the Riemann Zeros

It is shown that in Large-Nc QCD, two--point functions of local operators become Harmonic Sums. We comment on the properties which follow from this fact. This has led us to an aside observation concerning the zeros of the Riemann zeta--function seen from the point of view of Dispersion Relations in Quantum Theory.Comment: Invited talk at the Montpellier QCD 2010 Conferenc

Sharp bounds for harmonic numbers

In the paper, we first survey some results on inequalities for bounding harmonic numbers or Euler-Mascheroni constant, and then we establish a new sharp double inequality for bounding harmonic numbers as follows: For $n\in\mathbb{N}$, the double inequality -\frac{1}{12n^2+{2(7-12\gamma)}/{(2\gamma-1)}}\le H(n)-\ln n-\frac1{2n}-\gamma<-\frac{1}{12n^2+6/5} is valid, with equality in the left-hand side only when $n=1$, where the scalars $\frac{2(7-12\gamma)}{2\gamma-1}$ and $\frac65$ are the best possible.Comment: 7 page

Pengaruh Penambahan Onggok Difermentasi Acremonium charticola dan Antibiotik dalam Ransum terhadap Kualitas Litter dan Footpad Dermatitis Ayam Broiler

Penelitian ini bertujuan untuk mengkaji pengaruh pemberian pakan onggok differmentasi Acremonium charticola dan antibiotik terhadap kualitas litter dan footpad dermatitis (FPD). Penelitian dilaksanakan pada bulan April sampai dengan Juni 2016 di Kandang Unggas A Fakultas Peternakan dan Pertanian, Universitas Diponegoro, Semarang. Materi yang digunakan pada penelitian ini adalah 160 ekor day old chick broiler jantan strain Lohman dengan bobot awal rata – rata 41,30 ± 2,68 g yang dipelihara selama 28 hari. Kandang yang digunakan adalah kandang koloni berukuran 1 × 1 × 1,5 m dengan 20 unit petak percobaan. Pakan yang digunakan merupakan pakan yang disusun berdasarkan kebutuhan serta kandungan nutrisi ransum dengan penambahan onggok yang diferementasi dengan A. charticola dan antibiotik neomycin, dengan perlakuan sebagai berikut : T0 (kontrol), T1 (kontrol + antibiotik), T2 (kontrol + onggok yang terfementasi dengan A. charticola + antibiotik) dan T3 (kontrol + onggok yang terfementasi dengan A. charticola). Rancangan yang digunakan adalah rancangan acak lengkap dengan 4 perlakuan dan 5 ulangan. Parameter yang diukur meliputi kualitas litter (kadar air, pH dan NH3) serta footpad dermatitis, selanjutnya data dianalisis keragamannya pada taraf ketelitian 5% dilanjutkan dengan uji duncan dan non parametrik digunakan uji Kruskal Wallis. Hasil penelitian menunjukkan bahwa tidak ada pengaruh nyata (P>0,05) pada NH3 litter yaitu T0 = 9,00±2,24 T1 = 8,40±1,52 T2 =13,00±6,71 T3 = 12,00±4,47, (P>0,05) pada pH litter T0 = 8,18±0,08 T1 = 8,12±0,08 T2 = 8,04±0,25 T3 = 8,00±0,20 dan (P>0,05) pada Kadar Air litter T0 = 13,71±3,82 T1 = 1,40±0,89 T2 = 1,00±4,27 T3 = 1,40±0,89; tetapi berpengaruh nyata (P<0,05) pada scoring footpad dermatitis yaitu T0 = 0,00; T1 = 1,40; T2 = 1,00; T3 = 1,40. Simpulan yang diperoleh yaitu penambahan onggok difermentasi A. charticola dan antibiotik tidak menyebabkan penurunan kualitas litter tapi berpengaruh terhadap footpad dermatitis

Impossible?: Surprising solutions to counterintuitive conundrums

Princeton, New Jerseyxii, 235 p.: index; 24 c

Influence du vieillissement thermique sur les proprietes physico-chimiques et la reactivite des catalyseurs mono et bimetalliques a base de platine et/ou rhodium sur alumine ou sur cerine

SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

John Napier: life, logarithms, and legacy

John Napier (1550–1617) is celebrated today as the man who invented logarithms—an enormous intellectual achievement that would soon lead to the development of their mechanical equivalent in the slide rule: the two would serve humanity as the principal means of calculation until the mid-1970s. Yet, despite Napier’s pioneering efforts, his life and work have not attracted detailed modern scrutiny. John Napier is the first contemporary biography to take an in-depth look at the multiple facets of Napier’s story: his privileged position as the eighth Laird of Merchiston and the son of influential Scottish landowners; his reputation as a magician who dabbled in alchemy; his interest in agriculture; his involvement with a notorious outlaw; his staunch anti-Catholic beliefs; his interactions with such peers as Henry Briggs, Johannes Kepler, and Tycho Brahe; and, most notably, his estimable mathematical legacy. Julian Havil explores Napier’s original development of logarithms, the motivations for his approach, and the reasons behind certain adjustments to them. Napier’s inventive mathematical ideas also include formulas for solving spherical triangles, “Napier’s Bones” (a more basic but extremely popular alternative device for calculation), and the use of decimal notation for fractions and binary arithmetic. Havil also considers Napier’s study of the Book of Revelation, which led to his prediction of the Apocalypse in his first book, A Plaine Discovery of the Whole Revelation of St. John—the work for which Napier believed he would be most remembered