Modified projection algorithms for solving the split equality problems.

The split equality problem (SEP) has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Byrne and Moudafi (2013) proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively and performs an additional projection step onto two half-spaces in each iteration. We further propose a relaxation scheme for the self-adaptive projection algorithm by using projections onto half-spaces instead of those onto the original convex sets, which is much more practical. Weak convergence results for both algorithms are analyzed.

Simultaneous and semi-alternating projection algorithms for solving split equality problems.

In this article, we first introduce two simultaneous projection algorithms for solving the split equality problem by using a new choice of the stepsize, and then propose two semi-alternating projection algorithms. The weak convergence of the proposed algorithms is analyzed under standard conditions. As applications, we extend the results to solve the split feasibility problem. Finally, a numerical example is presented to illustrate the efficiency and advantage of the proposed algorithms.

An existence-uniqueness theorem and alternating contraction projection methods for inverse variational inequalities.

Let C be a nonempty closed convex subset of a real Hilbert space H with inner product 〈 ⋅ , ⋅ 〉 , and let f : H → H be a nonlinear operator. Consider the inverse variational inequality (in short, IVI ( C , f ) ) problem of finding a point ξ ∗ ∈ H such that f ( ξ ∗ ) ∈ C , 〈 ξ ∗ , v - f ( ξ ∗ ) 〉 ≥ 0 , ∀ v ∈ C . In this paper, we prove that IVI ( C , f ) has a unique solution if f is Lipschitz continuous and strongly monotone, which essentially improves the relevant result in (Luo and Yang in Optim. Lett. 8:1261-1272, 2014). Based on this result, an iterative algorithm, named the alternating contraction projection method (ACPM), is proposed for solving Lipschitz continuous and strongly monotone inverse variational inequalities. The strong convergence of the ACPM is proved and the convergence rate estimate is obtained. Furthermore, for the case that the structure of C is very complex and the projection operator P C is difficult to calculate, we introduce the alternating contraction relaxation projection method (ACRPM) and prove its strong convergence. Some numerical experiments are provided to show the practicability and effectiveness of our algorithms. Our results in this paper extend and improve the related existing results.

Molecular epidemic features and variation of rotavirus among children with diarrhea in Lanzhou, China, 2001-2006.

BACKGROUND: Human rotavirus (HRV) is the most common pathogen causing severe diarrhea among infants and young children worldwide. This study aims to understand rotavirus epidemiology and its variation in the period of 2001-2006 in Lanzhou, Gansu Province, China, and to provide an epidemiological basis for the development of rotavirus vaccine. METHODS: A total of 1019 stool specimens were collected from patients with acute diarrhea admitted to the First Hospital of Lanzhou University from 2001 to 2006, who were younger than 5 years old. Dako IDEIATM kits were used for detection of rotavirus, and RT-PCR was performed for determination of G serotype and P genotype of the rotavirus. RESULTS: Rotavirus was present in 51.6% (526) of the 1019 specimens. G serotype identified G3 at 40.9%, G2 14.6%, G1 22.2% and G9 1.9%. Mixed-G infection was observed in 4.4% and non-typeable infection 16.0%. P genotype was observed in 372 samples, of which P[8] accounted for 186 cases (50.0%), P[4] 72 cases (19.4%), mixed-P infection 2 cases (0.5%), and non-typeable cases 112 (30.1%). G3 was the most prevalent G serotype found in this study from 2001 to 2004, G2 was the most prevalent G serotype (34.4%) from 2004 to 2005, and G1 (61.5%) was the most prevalent strain from 2005 to 2006. G9 was detected in 10 cases (1.9%) and G4 was not detected during this 5-year period. P[8] was the most prevalent P genotype found over the 5 consecutive years of this study, although there was a significant transition of P genotype from 2004 to 2005 with P[4] (45%) identified as the predominant P genotype, followed by P[8] (22.1%). The predominant G-P combination was P[8]G1 (33.6%), followed by P[8]G3 (32.1%) and P[4]G2 (17.2%). Rotavirus diarrhea admissions peaked between October and December. Continuous surveillance showed that the incidence rate of rotavirus was the highest in infants aged 6-23 months, averaging 11.0-11.9 months. CONCLUSIONS: Five years of continuous surveillance showed that rotavirus remains the most significant viral agent causing diarrhea hospitalization among children under 5 years old in Lanzhou, China although the predominant strain of rotavirus varies between years. Mixed-G serotype infection also appears to occur at a relatively high rate in Lanzhou.

[Molecular epidemiology of human caliciviruses diarrhea among infants and young children in Lanzhou from December 2001 to June 2004].

OBJECTIVE: To investigate the characteristics of human caliciviruses (HuCV) diarrhea among infants and young children with acute diarrhea in Lanzhou, Gansu Province, China by using molecular epidemiologic techniques. METHODS: Stool specimens were collected from both outpatients and inpatients with acute diarrhea in Lanzhou. Enzyme-linked immunosorbant assay (ELISA) was used to detect rotavirus antigen (RVA). Reverse transcription-polymerase chain reactions (RT-PCR) were used to detect HuCV in stool specimens of RV ELISA (-). RESULTS: Of the stool specimens collected from 515 cases in Lanzhou from December 2001 to June 2004, 264 were RVA ELISA (+) and 251 were RVA ELISA (-). Among all cases who were RVA ELISA (-), 25 (9.96%) were found positive for HuCV. HuCV was detected in 12 of 133 cases (9.02%) from December 2001 to November 2002, no genotyping was performed for these cases. From July 2003 to June 2004 13 of 118 cases (11.02%) were found positive for HuCV, of whom 11 cases had Norwalk-like virus GII (NLV GII) infection and 2 cases had Sapporo-like virus infection (one case had combined infection with astrovirus) and no NLV GI was found. HuCV infection mainly occurred in children under 2 years of age and no seasonal cluster was found. CONCLUSION: HuCV is one of the major etiological agents of viral diarrhea among infants and young children in Lanzhou. NLV GII maybe the predominant genotype.

[Phylogenetic analysis of enterovirus 71 isolated from patients with hand, foot and mouth disease in Guangdong and Fujian provinces, 2000-2001].

OBJECTIVE: To identify enterovirus 71 (EV71) strains isolated from patients with hand, foot and mouth disease (HFMD) in Guangdong and Fujian provinces from 2000 to 2001 by using phylogenetic analysis. METHODS: All 25 samples were first tested for enteric viruses by RT-PCR using enterovirus specific primers EV-1 and EV-2, and then were identified for EV71 by RT-PCR using EV71 specific primers 159S and 162A. The amplicons of 485bp segment (part of the VP1 gene) were cloned into pGEM-T and sequenced. A phylogenetic tree was constructed by comparison of the sequences with other 12 EV71 strains isolated from China, Japan, Hungary, and the United States including the prototype BrCr. RESULTS: The positive rate of EV71 was about 20%. The sequence analysis showed that the new isolate (GZH2000) shared 94%-96% nucleotide identity with three strains isolated in 1998 and 2000, and 91% with a strain isolated in 1987 from Chinese mainland, but shared only 82%-84% homology with EV71 isolates studied abroad. CONCLUSIONS: EV71 is one of the important pathogens of HFMD in south China. The strains isolated from mainland were closely related with most isolates from Taiwan, but different from most EV71 strains reported abroad. The symptoms of EV71 infection in mainland were not as intensive as those described in Taiwan's outbreak.