Sums of Kloosterman sums in arithmetic progressions, and the error term in the dispersion method

We prove a bound for quintilinear sums of Kloosterman sums, with congruence conditions on the "smooth" summation variables. This generalizes classical work of Deshouillers and Iwaniec, and is key to obtaining power-saving error terms in applications, notably the dispersion method. As a consequence, assuming the Riemann hypothesis for Dirichlet $L$-functions, we prove a power-saving error term in the Titchmarsh divisor problem of estimating $\sum_{p\leq x}\tau(p-1)$. Unconditionally, we isolate the possible contribution of Siegel zeroes, showing it is always negative. Extending work of Fouvry and Tenenbaum, we obtain power-saving in the asymptotic formula for $\sum_{n\leq x}\tau_k(n)\tau(n+1)$, reproving a result announced by Bykovski\u{i} and Vinogradov by a different method. The gain in the exponent is shown to be independent of $k$ if a generalized Lindel\"of hypothesis is assumed

Sign changes of Kloosterman sums and exceptional characters

We prove that the existence of exceptional real zeroes of Dirichlet $L$-functions would lead to cancellations in the sum \sum_{p\leq x} \Kl(1, p) of Kloosterman sums over primes, and also to sign changes of \Kl(1, n), where $n$ runs over integers with exactly two prime factors. Our arguments involve a variant of Bombieri's sieve, bounds for twisted sums of Kloosterman sums, and work of Fouvry and Michel on sums of \left| \Kl(1, n)\right|.Comment: 11 page

Exponential sums with automatic sequences

We show that automatic sequences are asymptotically orthogonal to periodic exponentials of type $e_q(f(n))$, where $f$ is a rational fraction, in the P\'olya-Vinogradov range. This applies to Kloosterman sums, and may be used to study solubility of congruence equations over automatic sequences. We obtain this as consequence of a general result, stating that sums over automatic sequences can be bounded effectively in terms of two-point correlation sums over intervals.Comment: 14 page

Statistical distribution of the Stern sequence

We prove that the Stern diatomic sequence is asymptotically distributed according to a normal law, on a logarithmic scale. This is obtained by studying complex moments, and the analytic properties of a transfer operator.Comment: 13 page

Smooth-supported multiplicative functions in arithmetic progressions beyond the x1/2x^{1/2}-barrier

We show that smooth-supported multiplicative functions $f$ are well-distributed in arithmetic progressions $a_1a_2^{-1} \pmod q$ on average over moduli $q\leq x^{3/5-\varepsilon}$ with $(q,a_1a_2)=1$.Comment: 23 page

Expert system for on-board satellite scheduling and control

An Expert System is described which Rockwell Satellite and Space Electronics Division (S&SED) is developing to dynamically schedule the allocation of on-board satellite resources and activities. This expert system is the Satellite Controller. The resources to be scheduled include power, propellant and recording tape. The activities controlled include scheduling satellite functions such as sensor checkout and operation. The scheduling of these resources and activities is presently a labor intensive and time consuming ground operations task. Developing a schedule requires extensive knowledge of the system and subsystems operations, operational constraints, and satellite design and configuration. This scheduling process requires highly trained experts anywhere from several hours to several weeks to accomplish. The process is done through brute force, that is examining cryptic mnemonic data off line to interpret the health and status of the satellite. Then schedules are formulated either as the result of practical operator experience or heuristics - that is rules of thumb. Orbital operations must become more productive in the future to reduce life cycle costs and decrease dependence on ground control. This reduction is required to increase autonomy and survivability of future systems. The design of future satellites require that the scheduling function be transferred from ground to on board systems

STRUKTUR HISTOLOGIS GONAD IKAN GABUS (CHANNA STRIATA) BETINA

STRUKTUR HISTOLOGIS GONAD IKAN GABUS (Channa striata) BETINA ABSTRAKPenelitian ini bertujuan mengetahui struktur histologis gonad ikan gabus (Channa striata) betina. Sampel yang diambil dalam penelitian ini adalah gonad dari 5 ekor ikan gabus betina. Sampel kemudian dibuat menjadi preparat histologi dengan pewarnaan hematoksilin-eosin (HE) dan diteliti strukturnya menggunakan metode histologi eksplorasi. Hasil penelitian menunjukkan bahwa secara makroskopis dari 5 ekor ikan gabus betina yang digunakan terdapat 1 ekor ikan dengan ovarium pada fase mature (matang) dan 4 ekor ikan (ovariumnya berada pada fase spawning (mijah). Secara mikroskopis dari 5 ekor ikan gabus betina yang digunakan 1 ekor ikan berada pada fase maturing, 1 ekor ikan berada pada fase mature dan 3 ekor ikan ovariumnya berada pada fase postovulatory follicle. Kesimpulan dari penelitian ini adalah struktur ovarium ikan gabus terdiri atas stroma, vaskularisasi, dan folikel-folikel berkembang. Secara histologi ikan gabus memiliki 4 tahap perkembangan ovarium, immature, maturing, mature, dan spent/ recovering dan 7 tahap perkembangan oosit, chromatin nucleolar, early perinucleolar, late perinucleolar, yolk vesicle, early yolk granule, late yolk granule, dan spent ovary

Mobile Onsite drilling Waste Treatment (OWT) facilities - a solution for safer, cheaper, and environmentally friendly operations

Drilling mud waste, the by-product that generates from Drilling operation, should be treated to comply with GOI (Government of Indonesia) regulations. An oil and gas field in Sumatera Island operated by PT. X produced about 50,000 bbls water base mud per month, but the centralized mud treating facility (CMTF) was designed only to treat 30,000 bbls per month.Besides,transportation using vacuum truck is required to carry the waste from site to CMTF that creates potential of motor vehicle accidents while traveling.Using lean sigma framework with DMAIC methodology, a business case study was developed to find alternatives on how to manage the waste while also improving safety performance.We started with a pilot project, which is done very successfully, and then continuing with a full-scale implementation in the North area.Five (5) mobile (On Site Waste Treatment) OWT units with two (2) different technologies; electro-coagulation and advanced oxidation; are being operated to process drilling waste from the ground pit either while the rig is on location or after it is released. Each mobile OWT has capacity of 24,000 barrels/month. The effluent is regularly checked in the laboratory to ensure the output meets GOI regulations before release to environment. Implementing this Mobile OWT initiative has delivered added value to the Company of about US$375,000 over a nine (9) month period and improved HES compliance by reducing trips and mileage which in the end will reduce Motor Vehicle Crash (MVC) potential, especially when driving at night in our drilling waste operations.Future improvement could consider how to maintain the discharge solid while processing the mud waste from the same disposal pit; provide solid treating facility and application of closed loop drilling