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A Simple Proof That the Curl Defined as Circulation Density Is a Vector-Valued Function, and an Alternative Approach to Proving Stoke’s Theorem  [PDF]
David McKay
Advances in Pure Mathematics (APM) , 2012, DOI: 10.4236/apm.2012.21007
Abstract: This article offers a simple but rigorous proof that the curl defined as a limit of circulation density is a vector-valued function with the standard Cartesian expression.
On the Rotation of a Vector Field in a Four-Dimensional Space  [PDF]
Leonardo Simal Moreira
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.51015

Recently I published a paper in the journal ALAMT (Advances in Linear Algebra & Matrix Theory) and explored the possibility of obtaining products of vectors in dimensions higher than three [1]. In continuation to this work, it is proposed to develop, through dimensional analogy, a vector field with notation and properties analogous to the curl, in this case applied to the space IR4. One can see how the similarities are obvious in relation to the algebraic properties and the geometric structures, if the rotations are compared in spaces of three and four dimensions.

Molecular Identification and Sequence Analysis of Tobacco Leaf Curl Begomovirus from Jember, East Java, Indonesia
HAYATI Journal of Biosciences , 2008,
Abstract: Begomovirus had been proved as the causal agent of leaf curl disease in tobacco in Indonesia, or commonly in Indonesia called as penyakit krupuk tembakau. Association of Begomovirus with the disease was further confirmed by sequence analysis. Amplification of the virus was conducted following whitefly (Bemisia tabaci Genn.) transmission. Fragment of DNA 1.6 kb was amplified by polymerase chain reaction (PCR) located within the replication initiator protein gene and coat protein gene (top region). Conserved sequence of stem loop region was found, included nonanucleotide sequence TAATATTAC present in all geminiviruses. Begomovirus associated with leaf curl disease in tobacco showed the closest relationship with Ageratum yellow vein virus - Zimbabwe, a strain of Tobacco leaf curl virus from Southern Africa. It was also known that Begomovirus associated with leaf curl disease in tobacco from Jember, East Java was different from other Indonesian Begomoviruses reported earlier.
The effects of the parents’ genotype on susceptibility to leaf curl (Taphrina deformans (Berk.) Tul) of vineyard peach hybrid seedlings
Zec Gordan,?oli? Slavica,Jankovi? Zoran,?urovi? Sne?ana
Genetika , 2007, DOI: 10.2298/gensr0701047z
Abstract: Leaf curl is one of the peach diseases with the most economically important impact, because very strong infection can cause total defoliation. Susceptibility to a leaf curl was examined from the period 1994-1998 in a collection of selected vineyard peach genotypes and newly peach and nectarine cultivars. Selected low susceptible genotypes (vineyard peach GR/65/87 and processing peach Villa Ada) were used in cross-pollination with differently susceptible genotypes. The process produced more than 250 seedlings of F1 progeny from few combinations of the parents. Susceptibility of hybrid seedlings to the leaf curl pathogen was investigated several years in the open field, without application of pesticide. More types of inheritance of examined characteristic were determinate in the progenies from different combinations of the parents. The results agree with polygenic inheritance. .
Relationship of Cotton Leaf Curl Virus Symptoms with Virus Concentration and Epitope Profile
Saif Khalid,Hussain Shah,Muhammad Asif Masood
Pakistan Journal of Biological Sciences , 1999,
Abstract: Vein thickening, enation formation and curling of leaves (upward or downward) are characteristic symptoms of cotton leaf curl virus, a whitefly (Bemisia tabaci) transmitted geminivirus, in cotton. To ascertain the effect of virus titer on type of curling and their relationship with epitope profile we determined virus concentration in 26 samples (13 each upward and downward curling) and established epitope profile of 34 samples (17 each) by TAS-ELISA using polyclonal antisera to Indian Cassava Mosaic Virus (ICMV) and Monoclonal Antibodies (MAbs) to African Cassava Mosaic Virus (ACMC) & ICMV and Okra Leaf Curl Virus (OLCV). No relationship between virus concentration and epitope profile was found with type of symptoms.
Cotton Leaf Curl Disease: Measuring and Analyzing its Epidemics Using GIS
Athar Nadeem,Merritt R. Nelson,Thomas V. Orum,Ijaz Parvez
Pakistan Journal of Biological Sciences , 2001,
Abstract: Cotton leaf curl disease occurred throughout the province of Punjab during the year 1996, but there were patches where it was less severe and other patches where it was very severe. Nine varieties were planted in Mian Channun project area. CIM-240 was predominant variety through out cotton growing region of the Punjab There were varietal differences in both incidence and severity. To eliminate the possibility of varietal effects on the spatial pattern, kriging was done with only those fields planted with CIM-240. There were not enough points to give a broad coverage of the area, but the basic spatial pattern of incidence was the same as when all varieties except CIM-1100 are included in the analysis. Any influence of variety was evidently randomly distributed across the landscape so that the spatial pattern of the disease on CIM-240 was similar to the spatial pattern on all the varieties combined. This might not always be so in years when there are strong regional differences in the selection of varieties. There was a strong correlation (r = 0.962) between incidence and severity and the spatial pattern of severity was quite similar to that of incidence.
Quick detection of Cotton leaf curl virus
Indian Phytopathology , 2012,
Liliam F. Oliveira,Thiago T. Matta,Daniel S. Alves,Marco A.C. Garcia
Journal of Sports Science and Medicine , 2009,
Abstract: Incline Dumbbell Curl (IDC) and Dumbbell Preacher Curl (DPC) are two variations of the standard Dumbbell Biceps Curl (DBC), generally applied to optimize biceps brachii contribution for elbow flexion by fixing shoulder at a specific angle. The aim of this study is to identify changes in the neuromuscular activity of biceps brachii long head for IDC, DPC and DBC exercises, by taking into account the changes in load moment arm and muscle length elicited by each dumbbell curl protocol. A single cycle (concentric-eccentric) of DBC, IDC and DPC, was applied to 22 subjects using a submaximal load of 40% estimated from an isometric MVC test. The neuromuscular activity of biceps brachii long head was compared by further partitioning each contraction into three phases, according to individual elbow joint range of motion. Although all protocols elicited a considerable level of activation of the biceps brachii muscle (at least 50% of maximum RMS), the contribution of this muscle for elbow flexion/extension varied among exercises. The submaximal elbow flexion (concentric) elicited neuro muscular activity up to 95% of the maximum RMS value during the final phase of IDC and DBC and 80% for DPC at the beginning of the movement. All exercises showed significant less muscle activity for the elbow extension (eccentric). The Incline Dumbbell Curl and the classical Dumbbell Biceps Curl resulted in similar patterns of biceps brachii activation for the whole range of motion, whereas Dumbbell Preacher Curl elicited high muscle activation only for a short range of elbow joint angle
Transcript mapping of Cotton leaf curl Burewala virus and its cognate betasatellite, Cotton leaf curl Multan betasatellite
Akbar Fazal,Briddon Rob W,Vazquez Franck,Saeed Muhammad
Virology Journal , 2012, DOI: 10.1186/1743-422x-9-249
Abstract: Background Whitefly-transmitted geminiviruses (family Geminiviridae, genus Begomovirus) are major limiting factors for the production of numerous dicotyledonous crops throughout the warmer regions of the world. In the Old World a small number of begomoviruses have genomes consisting of two components whereas the majority have single-component genomes. Most of the monopartite begomoviruses associate with satellite DNA molecules, the most important of which are the betasatellites. Cotton leaf curl disease (CLCuD) is one of the major problems for cotton production on the Indian sub-continent. Across Pakistan, CLCuD is currently associated with a single begomovirus (Cotton leaf curl Burewala virus [CLCuBuV]) and the cotton-specific betasatellite Cotton leaf curl Multan betasatellite (CLCuMuB), both of which have recombinant origins. Surprisingly, CLCuBuV lacks C2, one of the genes present in all previously characterized begomoviruses. Virus-specific transcripts have only been mapped for few begomoviruses, including one monopartite begomovirus that does not associate with betasatellites. Similarly, the transcripts of only two betasatellites have been mapped so far. The study described has investigated whether the recombination/mutation events involved in the evolution of CLCuBuV and its associated CLCuMuB have affected their transcription strategies. Results The major transcripts of CLCuBuV and its associated betasatellite (CLCuMuB) from infected Nicotiana benthamiana plants have been determined. Two complementary-sense transcripts of ~1.7 and ~0.7 kb were identified for CLCuBuV. The ~1.7 kb transcript appears similar in position and size to that of several begomoviruses and likely directs the translation of C1 and C4 proteins. Both complementary-sense transcripts can potentially direct the translation of C2 and C3 proteins. A single virion-sense transcript of ~1 kb, suitable for translation of the V1 and V2 genes was identified. A predominant complementary-sense transcript was also confirmed for the betasatellite. Conclusions Overall, the transcription of CLCuBuV and the recombinant CLCuMuB is equivalent to earlier mapped begomoviruses/betasatellites. The recombination events that featured in the origins of these components had no detectable effects on transcription. The transcripts spanning the mutated C2 gene showed no evidence for involvement of splicing in restoring the ability to express intact C2 protein.
Identificación del gen Ty-3, de resistencia a begomovirus, en accesiones de Solanum lycopersicum L
Due?as Hurtado,Francisco; álvarez Gil,Marta; Moya López,Carlos; Martínez Zubiaur,Yamila;
Cultivos Tropicales , 2011,
Abstract: tomato yellow leaf curl disease is one of the most important problems affecting tomato cultivation in most part of the cuban growing areas and in other countries. the casual agent is the tomato yellow leaf curl virus (tylcv). at the moment several genes related with the resistance have been described. the genes ty-1, ty-2 and ty-3 are those that more they have been used in the plant breeding programs of the species. in cuba, vyta is only variety that had ty-1 gene and other accessions carrying the ty-2 gene. the amplification of the gene ty-3 was carried out for pcr and were used the specific primers fluw-25r and fluw-25f. in this work the presence of the band related with the resistant pattern of the gene ty-3 was identified in one that six characterized accessions
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