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

Phase transitions in least-effort communications

Original article can be found at: http://iopscience.iop.org Copyright IOP PublishingWe critically examine a model that attempts to explain the emergence of power laws (e.g., Zipf's law) in human language. The model is based on the principle of least effort in communications—specifically, the overall effort is balanced between the speaker effort and listener effort, with some trade-off. It has been shown that an information-theoretic interpretation of this principle is sufficiently rich to explain the emergence of Zipf's law in the vicinity of the transition between referentially useless systems (one signal for all referable objects) and indexical reference systems (one signal per object). The phase transition is defined in the space of communication accuracy (information content) expressed in terms of the trade-off parameter. Our study explicitly solves the continuous optimization problem, subsuming a recent, more specific result obtained within a discrete space. The obtained results contrast Zipf's law found by heuristic search (that attained only local minima) in the vicinity of the transition between referentially useless systems and indexical reference systems, with an inverse-factorial (sub-logarithmic) law found at the transition that corresponds to global minima. The inverse-factorial law is observed to be the most representative frequency distribution among optimal solutions.Peer reviewe

Impossible?: Surprising solutions to counterintuitive conundrums

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