A Search for Patterns in a Sequence of Integers: Proving Trends in a Recurrence Relation

Let {f(n} be the sequence of integers determined by the recurrence relation f(n+2) equivalent to 2f(n+1) - f(n) (mod(n+2)) with f(n) greater than or equal to 0 and less than n for every integer n greater than or equal to m, where m is a certain positive integer with initially assigned arbitrary integers f(m) and f(m+1). We investigate how the sequence {f(n} increases or decreases. We call a maximal increasing or decreasing subsequence of consecutive elements of the sequence a run. We show that each run is an arithmetic progression and that the common difference in an increasing run is one more than the common difference in the previous increasing run, and similary for decreasing runs

PENGARUH PENYERTAAN MODAL PEMERINTAH DAERAH TERHADAP KINERJA PERUSAHAAN DAERAH AIR MINUM : Penelitian pada PDAM di Kabupaten/Kota Jawa Barat Tahun 2012 – 2014

Penelitian ini bertujuan untuk mengetahui bagaimana penyertaan modal pemerintah daerah, kinerja Perusahaan Daerah Air Minum (PDAM), dan pengaruh penyertaan modal pemerintah daerah terhadap kinerja PDAM pada PDAM di Kabupaten/Kota Jawa Barat Tahun 2012 – 2014. Sampel ditentukan berdasarkan teknik purposive sampling. Pengujian hipotesis pada penelitian ini menggunakan analisis regresi data panel. Penyertaan modal pemerintah daerah diukur dengan nilai buku penyertaan modal pemerintah daerah terhadap PDAM. Sedangkan kinerja PDAM diukur dengan menjumlahkan skor pada tiap aspek balanced scorecard. Dari hasil pengujian hipotesis terdapat pengaruh penyertaan modal pemerintah daerah terhadap kinerja PDAM pada PDAM di Kabupaten/Kota Jawa Barat selama tahun 2012 – 2014. Artinya semakin naik jumlah penyertaan modal pemerintah daerah terhadap PDAM diprediksikan akan meningkatkan kinerja PDAM.----------This study aims to find out how the local government capital participation, the performance of Regional Water Company (PDAM), and the influence of local government capital participation on PDAM performance in PDAM in West Java regency/city during 2012 - 2014. The sample is determined by purposive sampling technique. Hypothesis testing in this study using panel data regression analysis. The participation of local government capital is measured by the book value of local government capital participation on PDAM. While the performance of PDAM is measured by summing the scores on each aspect of the balanced scorecard. From the result of hypothesis testing, there is an influence of local government capital participation on PDAM performance in PDAM in West Java regency/city during 2012 - 2014. It means that increasing amount of local government capital participation to PDAM is predicted to improve PDAM performance

Time-optimal Control of Petrowsky Systems with Infinitely Many Variables and Control-state Constraints

In this paper, the time-optimal control problem for n × n differential systems of Petrowsky type with infinitely many variables and control-state constraints are considered. For some different cases of the observation, the necessary optimality conditions of optimal control are obtained by using the generalized Dubovitskii-Milyutin Theorem (Theorem 1.8.1, [1]). Key Words: Time-optimal control problem; Petrowsky systems; Dubovitskii-Milyutin method; Canonical approximations; Optimality condition

The Timoshenko Three-Beams Technique To Estimate The Main Elastic Moduli Of Orthotropic Homogeneous Materials

A New developed technique to estimate the necessary six elastic constants of homogeneous laminate of special orthotropic properties are presented in this paper for the first time. The new approach utilizes the elasto-static deflection behavior of composite cantilever beam employing the famous theory of Timoshenko. Three extracted strips of the composite plate are tested for measuring the bending deflection at two locations. Each strip is associated to a preferred principal axis and the deflection is measured in two orthogonal planes of the beam domain. A total of five trails of testing is accomplished and the numerical results of the stiffness coefficients are evaluated correctly under the contribution of the macromechanics and the approximate bending theory. To insure the validity of the new approach, separate individual tensile tests are performed, and the corresponding results are compared. Excellent agreements are obtained between the different approaches. The ease, simple and accurate predictions are well confident by the new techniqu

Optimality conditions for differential system of Petrowsky type with infinite number of variables and boundary control

AbstractIn this paper, we study the optimal control problem for an n×n coupled Petrowsky type system involving a 2ℓ-th order self-adjoint elliptic operator with an infinite number of variables and constrained boundary control acting through Neumann conditions. Also, we derived the necessary and sufficient conditions of optimality for two types of performance index (quadratic one, general integral form).By using standard Lions’s arguments [J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, vol. 170, Springer-Verlag, 1971] we proved the existence of a solution to the n×n coupled Petrowsky system and we derived optimality conditions for the optimal control problem with a quadratic performance index. In the case of the general integral form of the performance index we applied Dubovitskii–Milyutin’s formalism earlier used in Kotarski [W. Kotarski, Some problems of optimal and pareto optimal control for distributed parameter systems, Reports of Silesian University Katowice, Poland, 1997, no. 1668]. Finally, we provided some special cases

Engineering, Geophysical Investigation of a Multistory Building, at Hilla, Iraq, Utilizing the MASW Method

The Multi-Channel Method for Surface Waves (MASW) was used to estimate the average velocity of shear waves in order to construct an engineering structure and its relationship to bearing capacity, foundation depth and soil thickness in this construct in the center of Hilla city. Active MASW was used in this study which allows us to measure the apparent dispersion curve or the phase velocity within the frequency range from 5 to 70 Hz, which gives information about the shallow layers (25-50 m) and depending on the ground hardness and spreading length. Where it was found that this area consists of two layers and each layer has a shear velocity, as the first layer has shear velocity (171.891) m/sec and the depth (8.244) m and the second layer has shear velocity (274.788) m/sec and the maximum bearing capacity value relative to the depth of the foundation is 1, 2 and 3 is 4.46, 5.27 and 5.96 T/m2 respectively. According to this study, this area is suitable for constructing an engineering structure on it

Association between VNTR Polymorphism in Promoter Region of Prodynorphin (PDYN) Gene and Methamphetamine Dependence

AIM: Prodynorphin (PDYN; OMIM: 131340) is the precursor of the dynorphin related peptides which plays an important role in drug abuse. Previous studies have been shown that the expression of PDYN is regulated by a genetic polymorphism of VNTR in the promoter region of the gene.MATERIALS AND METHODS: The present case-control study was performed on 52 (41 males, 11 females) methamphetamine dependence patients and 635 (525 males, 110 females) healthy blood donors frequency matched with the patients according to age and gender, as a control group was participated in the study.RESULTS: The genotypes of VNTR PDYN polymorphism were determined using PCR method. The HL (OR = 1.22, 95%CI: 0.67-2.20, P = 0.500) and LL (OR = 0.86, 95%CI: 0.28-2.57, P = 0.792) genotypes does not alter the risk of methamphetamine dependence, in comparison with the HH genotypes.CONCLUSION: The present study revealed no association between the VNTR polymorphism in the promoter region of the PDYN gene and methamphetamine dependence risk

Self-assessed Oral Health Awareness and Attitude of the First and Final Year Undergraduate Medical and Dental Students in India

Aims and Objective: To compare the attitude and awareness of dental and medical students in the first and the final academic years and to trace the change in their attitude and awareness towards oral health; to also bring out differences/similarities in response to the questionnaire based on gender. Materials and methods: A modified version of HU-DBI questionnaire was used to conduct the survey in medical and dental colleges of India. A total of 279 students were recruited in the study. The data collected concerned the oral hygiene awareness and attitude, dental complaints and previous visits to dentists. Results: Significant differences were found for 9 of 17 items, reflecting an increased awareness and improved attitude toward oral health in the final year dental students as compared to the first year dental students. The dental students exhibited better awareness than the medical students irrespective of gender. Conclusion: Significant improvement was found in the awareness and attitude of the final year dental students as compared to the first year dental students. This change was marginal in the medical students

Orthodontic Treatment Considerations in Pregnancy: An Insight

Introduction: This article presents an insight on little known fact regarding orthodontic treatment in pregnancy and to find literature support in favor regarding orthodontic treatment during pregnancy. Literature was reviewed extensively to get results dental and orthodontic treatment during pregnancy. Discussion: Nowadays there are many adult patients seekingorthodontic treatment because of increase in awareness. In these adult patients, there are many pregnant females coming to orthodontist for treatment or a lady getting pregnant during the treatment. ‘Can a pregnant woman continue with orthodontic treatment or can she start with orthodontic treatment during pregnancy?’ This is a difficult question to answer but ‘Yes’, pregnant women can go for orthodontic treatment but with precautions. Present article gives us the information how to go about the treatment in pregnant women, the precautions to be taken, effect of drugs and hormonal changes on orthodontic treatment. Conclusion: Pregnant women can go for orthodontic treatment but with some precaution and some systemic and local condition limit the treatment modalities

THE STRUCTURAL MODIFICATION CAUSES THE ENHANCEMENT OF ANALGESIC ACTIVITY OF 4-(4′ CHLORO –PHENYL)-4- HYDROXY PIPERIDINE

Objective- The outstanding  position of piperidine analogues  has proven them an important core in the structures of pharmaceutically active molecules, naturally occurring alkaloids, pharmaceuticals and as synthetic intermediates with interesting biological, physical and pharmacological behaviors. The  piperidine ring containing compound like pethidine having strong opiod analgesic activity, more potent than codein and controls the pain of smooth muscle spasm. Because of having similarity in structure the present study was aimed to estimate the analgesic activity of synthesized derivatives of 4-(4′-Chlorophenyl)-4-hydroxy piperidine.Method- The present study was conducted in animal model, mice by using Pethidine as standard drug. For which the Eddy's hot plate method was adopted and analgesia ( mean increase in latency)  was observed.Result- The result showed the more prominent response of substituted compound than the parent one 4-(4′-Chlorophenyl)-4-hydroxy piperidine†and it was studied that alteration in the molecule structure is accountable for  a better analgesic response.Conclusion- The studies proved the positive pharmacological responsiveness of the combination of 4-(4′-Chlorophenyl)-4-hydroxy piperidine with phencyl halides. These synthesized derivatives will establish as potent analgesics.KEY WORDS:AlkaloidsOpiodAnalgesicPiperidin