A lower bound for the size of a Minkowski sum of dilates

Let A be a finite non-empty set of integers. An asymptotic estimate of the size of the sum of several dilates was obtained by Bukh. The unique known exact bound concerns the sum |A + k·A|, where k is a prime and |A| is large. In its full generality, this bound is due to Cilleruelo, Serra and the first author. Let k be an odd prime and assume that |A| > 8kk. A corollary to our main result states that |2·A + k·A|=(k+2)|A|-k2-k+2. Notice that |2·P+k·P|=(k+2)|P|-2k, if P is an arithmetic progression.Postprint (author's final draft

Identifikasi cemara mikroba pada saus tomat isi ulang yang digunakan di tiga kota makassar universitas indonesia timur kota makassar

Saus tomat merupakan bahan makanan isi ulang yang sering digunakan setiap hari, baik di rumah tangga maupun di tempat-tempat umum seperti kantin, restoran dan sebagainya. Namun dalam kehidupan sehari-hari, perhatian terhadap kebersian kecap terkadang diabaikan. Ini tentu saja merupakan salah satu faktor penurunan tingkat kesehatan masyarakat jika kecom mengkisumsis yang telah terkontaminasi oleh berbagai jenis mikroba. Tujuan penelitian ini adalah untuk mengetahui apakah ada kandungan mikroba yang terkandung dalam isi ulang saus tomat yang digunakan dalam tiga (3) rumah. Makan UIT. Metode yang digunakan dalam penelitian ini adalah tipe deskriptif survei sederhana: analisis laboratorium untuk mengetahui ada tidaknya mikroba dalam isi ulang saus tomat. Berdasarkan penelitian tersebut diharapkan dapat lebih mamperhatikan manajer kantin atau menjaga kebersihan kantin agar kecap isi ulang yang disajikan tidak terkontaminasi oleh bakteri Actvat

Adaptive mesh refinement for eddy current testing finite element computations

International audienceThis paper deals with an adaptive mesh refinement method applied to 3D eddy current non-destructive testing (ECNDT) computations by finite element method. In ECNDT finite element simulation having a “good mesh” isparticularly crucial since the geometry can be complex and abrupt field variations can be encountered. This appropriate mesh allows to obtain accurate solution with a reduced number of elements and so a reasonable computational time. Creating such a mesh is delicate and could necessitate a prohibitive development time for a numerical software user. An approach to overcome this problem is to use an adaptive meshing technique. In this paper the principle of Ligurian is used as error estimator and applied in a general computation processing loop. An example based on a benchmark is presented. This work takes place within the framework of the development of an ECNDT numerical simulation environment for computer-aided design

A lower bound for the size of a Minkowski sum of dilates

Let A be a finite non-empty set of integers. An asymptotic estimate of the size of the sum of several dilates was obtained by Bukh. The unique known exact bound concerns the sum |A + k·A|, where k is a prime and |A| is large. In its full generality, this bound is due to Cilleruelo, Serra and the first author. Let k be an odd prime and assume that |A| > 8kk. A corollary to our main result states that |2·A + k·A|=(k+2)|A|-k2-k+2. Notice that |2·P+k·P|=(k+2)|P|-2k, if P is an arithmetic progression

Asna al-Mathaalib : syarah raudha al-thaalib

Kitab Asna al-Mathalib Syarh Rawdh al-Thalib merupakan sebuah kitab fiqh mazhab al-Syafi?i. Kitab Asna al-Mathalib ini disusun sebagai huraian (syarah) bagi kitab Rawdh al-Thalib karya al-?Allamah Ismail bin Abu Bakr Abdullah al-Muqri al-Yamani (837H) yang terkenal dengan gelaran Ibn al-Muqri