On Commutative Rings Whose Prime Ideals Are Direct Sums of Cyclics

In this paper we study commutative rings $R$ whose prime ideals are direct sums of cyclic modules. In the case $R$ is a finite direct product of commutative local rings, the structure of such rings is completely described. In particular, it is shown that for a local ring $(R, \cal{M})$, the following statements are equivalent: (1) Every prime ideal of $R$ is a direct sum of cyclic $R$-modules; (2) ${\cal{M}}=\bigoplus_{\lambda\in \Lambda}Rw_{\lambda}$ and $R/{\rm Ann}(w_{\lambda})$ is a principal ideal ring for each $\lambda \in \Lambda$;(3) Every prime ideal of $R$ is a direct sum of at most $|\Lambda|$ cyclic $R$-modules; and (4) Every prime ideal of $R$ is a summand of a direct sum of cyclic $R$-modules. Also, we establish a theorem which state that, to check whether every prime ideal in a Noetherian local ring $(R, \cal{M})$ is a direct sum of (at most $n$) principal ideals, it suffices to test only the maximal ideal $\cal{M}$.Comment: 9 Page

The Disease Pattern and Utilisation of Health Care Services in Pakistan

Health is an important aspect of human life. In general terms, better health status of individuals reflects reduced illnesses, low level of morbidity, and less burden of disease in a given population. It is widely recognised that improved health not only lowers mortality, morbidity and level of fertility, but also contributes to increased productivity and regular school attendance of children as a result of fewer work days lost due to illness, which in turn have implications for economic and social well-being of the population at large. Hence investing in health is vital for promoting human resource development and economic growth in a country [World Bank (1993)]. A view of Pakistan’s health profile indicates that the sector has expanded considerably in terms of physical infrastructure and its manpower in both the public and private sector. This has contributed to some improvement in selected health status indicators over the years. However, the public health care delivery system has been inadequate in meeting the needs of the fast growing population and in filtering down its benefits to the gross-root level. As such, Pakistan still has one of the highest rates of infant and child mortality, total fertility and maternal mortality when compared with many other countries in the Asian region [UNDP (2000)]. Due to low priority given to social sector development in the past and low budgetary allocations made to the health sector, the evidence shows that mortality and morbidity indices have not reduced to the desired level and large gaps remain in the quality of care indicators, especially in rural areas [Federal Bureau of Statistics (2000)]. High levels of infant and child mortality and fertility in Pakistan point towards the fact that health and illness problems are severe for young children and mothers.

The radiated fields of the fundamental mode of photonic crystal fibers

The six-fold rotational symmetry of photonic crystal fibers has important manifestations in the radiated fields in terms of i) a focusing phenomena at a finite distance from the end-facet and ii) the formation of low-intensity satellite peaks in the asymptotic far field. For our study, we employ a surface equivalence principle which allows us to rigorously calculate radiated fields starting from fully-vectorial simulations of the near field. Our simulations show that the focusing is maximal at a characteristic distance from the end-facet. For large-mode area fibers the typical distance is of the order 10 Lambda with Lambda being the pitch of the triangular air-hole lattice of the photonic crystal fiber.Comment: 6 pages including 4 figures. Accepted for Opt. Expres

Kesan Latihan Wacana Secara Sistematik Terhadap Kemahiran Menulis Esei Argumentatif

Penyelidikan ini cuba mendapatkan data tentang Kesan Latihan Wacana Secara Sitematik (LWS S) Terhadap Kemahiran Menulis di kalangan pelaj ar-pelaj ar tingkatan empat, di dua buah sekolah menengah harian di daerah Hulu Langat, dan sebuah sekolah menengah harian di daerah Banting, Selangor Darul Ehsan. Tujuan penyelidikan ini dibuat adalah untuk mengenal pasti sama ada berlaku perubahan tingkah laku pembelajaran atau pun tidak dalam kalangan sampel penyelidikan ini hasil daripada LWSS. Data penyelidikan dikumpulkan melalui dua fasa, iaitu fasa ujian pra (UB) clan fasa ujian pasca (US) untuk mengenal pasti kesan LWSS terhadap kemahiran pembinaan ayat yang berwacanakan wacana argumentatif, penganalisian ciri-ciri wacana, penggunaan penanda wacana dan penulisan esei argumentatif. Soal selidik digunakan oleh penyelidik untuk mendapatkan maklumat tentang pencapaian BM dalam peperiksaan Penilaian Menengah Rendah (PMR) dan tentang pembelajaran iii BM. Item-item dalam ujian pra dan pasca direkabentuk untuk mendapatkan data tentang penguasaan sampel bagi aspek penulisan, penganalisian, penggunaan dan penulisan wacana argumentatif Kerangka teoretis penyelidikan ini berdasarkan Teori Matlamat Wacana Kineavy (1971) dengan sokongan Model Wacana Toulmin's (1998) dan Gaya Penulisan Litullipe (1996). Teori dm Model ini diubahsuai dengan pembentukan Kerangka Kollseptual Penyelidikan untuk memperoleh data yang tepat berdasarkan Ujian Pasca-Ujian Pra setelah olahan dilakukan terhadap sampel. Hasil perkiraan ujian-t menunjukkan bahawa terdapat perbezaan yang signifikan antara pelajar yang berpencapaian tinggi (PBT) dengan pelajar yang berpencapaian sederhana (PBS) d m pelajar yang berpencapaian rendah (PBR) dalam aspek pembinaan ayat argumentatif, penggunaan penanda wacana dan penulisan esei argumentatif . Analisis varian (ANOVA) pula digunakan untuk menunjukkan perbezaan yang signifikan antara kumpulan PBT dengan PBS dan PBR dan dalam kumpulan. Walau bagaimampun, PBT telah menunjukkan pencapaian yang lebih tinggi jika dibandingkan dengan PBS dm PBR. Untuk mengukuhkan dapatan, penyelidik telah menggunakan data kualitatif bagi menyokong dapatan daripada data kuantitatif. Ternyata bahawa, LWSS amat sesuai digunakan sebagai modul latihan bagi penulisan pelbagai jenis esei. Keputusan penyelidikan menunjukkan bahawa LWSS boleh diseslraikan bagi golongan pelajar yang cerdas dan kurang cerdas. Oleh sebab itu, jika LWSS digunakan dalam latihan dan pengajaran dan pembelajaran BM, teknik ini akan menjadi salah satu teknik yang menarik dan menyeronokkan para pelajar. Seterusnya, dapatan penyelidikan ini telah menghasilkan dua penemuan bam, iaitu teknik dan strategi penganalisian ayat berdasarkan Rajah Pohon (RP) dan Unsur Bawahan Terdekat (UBT) dan strategi penyepaduan kemahiran bahasa dengan strategi penulisan esei secara kelas, kumpulan kecil, penulisan individu, dan penulisan komuniti. Berdasarkan elemen Penilaian Berasaskan Sekolah (PBS, 2003), penemuan ini amat berfaedah dm sangat bermanfaat untuk digunakan oleh guru-guru di seluruh Malaysia, khususnya dalarn kemahiran menulis

CASE STUDY ON THE NEEDS ANALYSIS OF VOCATIONAL MEDICAL LAB STUDENTS AT THE NATIONAL INSTITUTE FOR TECHNOLOGY

The development of vocational education programs in Kurdistan is considered a potential solution to enhance the region's human resources. This development is closely linked to the development of English language proficiency in Kurdistan. The Ministry of Higher Education and Scientific Research has focused on enhancing the communicative abilities of vocational education students in English, particularly in listening, reading, writing, and speaking. This study examines the needs assessment of English for Specific Purposes (ESP) courses for educational students, aiming to identify learning objectives and needs. Data were gathered through questionnaires and interviews, revealing that students face difficulties in active communication skills (40%), grammar (15%), reading comprehension (25%), content comprehension (10%), and writing (10%). Specific areas of English language use in technology were identified, including English media (40%), crosswords (20%), dialogue content (20%), and multiple-choice exercises (20%). The study's findings contribute to understanding the learning requirements and objectives necessary for effective English language education. They emphasize the importance of addressing students' reading, writing, grammar, and other requirements to prepare them for future challenges