Consider the multiplication operator MB in $L^2(\mathbb{T})$, where the symbol B is a finite Blaschke product. In this article, we characterize the commutant of MB in $L^2(\mathbb{T})$. As an application of this characterization result, we explicitly determine the class of conjugations commuting with $M_{z^2}$ or making $M_{z^2}$ complex symmetric by introducing a new class of conjugations in $L^2(\mathbb{T})$. Moreover, we analyse their properties while keeping the whole Hardy space, model space and Beurling-type subspaces invariant. Furthermore, we extended our study concerning conjugations in the case of finite Blaschke products.

Noting a curious link between Andrews’ even-odd crank and the Stanley rank, we adopt a combinatorial approach building on the map of conjugation and continue the study of integer partitions with parts separated by parity. Our motivation is twofold. Firstly, we derive results for certain restricted partitions with even parts below odd parts. These include a Franklin-type involution proving a parametrized identity that generalizes Andrews’ bivariate generating function, and two families of Andrews–Beck type congruences. Secondly, we introduce several new subsets of partitions that are stable (i.e. invariant under conjugation) and explore their connections with three third-order mock theta functions $\omega (q)$, $\nu (q)$, and $\psi ^{(3)}(q)$, introduced by Ramanujan and Watson.

Presence of antimicrobial resistance (AMR) genes in Escherichia coli inhabiting anthropogenic rivers is an important public health concern because plasmid-mediated AMR genes can easily spread to other pathogens by horizontal gene transfer. Besides β-lactams, quinolones and aminoglycosides are the major antibiotics against E. coli. In the present study, we have investigated the presence of plasmid-mediated quinolone resistance (PMQR) and aminoglycoside resistance genes in E. coli isolated from a major river of northern India. Our results revealed that majority of the strains were phenotypically susceptible for fluoroquinolones and some aminoglycosides like amikacin, netilmicin, tobramycin and gentamicin. However, 16.39% of the strains were resistant for streptomycin, 8.19% for kanamycin and 3.30% for gentamicin. Of the various PMQR genes investigated, only qnrS1 was present in 24.59% of the strains along with ISEcl2. Aminoglycoside-resistance genes like strA-strB were found to be present in 16.39%, aphA1 in 8.19% and aacC2 in only 3.30% of the strains. Though, no co-relation was observed between phenotypic resistance for fluorquinolones and presence of PMQR genes, phenotypic resistance for streptomycin, kanamycin and gentamicin exactly co-related with the presence of the genes strA-strB, aphA1 and aacC2, respectively. Moreover, all the AMR genes discerned in aquatic E. coli were found to be situated on conjugative plasmids and, thus easily transferrable. Our study accentuates the importance of routine surveillance of urban rivers to curtail the spread of AMR genes in aquatic pathogens.

Assume that $G$ is a finite group and $H$ is a 2-nilpotent Sylow tower Hall subgroup of $G$ such that if $x$ and $y$ are $G$-conjugate elements of $H\cap G^{\prime }$ of prime order or order 4, then $x$ and $y$ are $H$-conjugate. We prove that there exists a normal subgroup $N$ of $G$ such that $G=HN$ and $H\cap N=1$.

In 1968 Emmerick proposed the existence of a present stem type D. It is shown here from morphophonological patterning that his category contains two subtypes, temporarily labelled D1 and D2. By comparing vocalic contractions from the nominals with the D1 endings, it is clear that the D1 stems end synchronically in -a- and take the regular type A endings. The D2 stem vowel in contrast, behaves partly like nominal stems in -a-, and partly like stems in -i-. By reviewing contraction evidence relating to all vowels, it is shown that the D2 stems end synchronically, albeit abstractly, in -e- and take the regular type A endings. Two further verbs from Emmerick's type C are shown also to end in -e- and take the regular endings.

Young orange [Citrus sinensis (L.) Osbeck ‘Pineapple sweet orange’] trees are more sensitive to bromacil (5-bromo-3-sec-butyl-6-methyluracil) than young mandarin (Citrus reticulata Blanco ‘Cleopatra mandarin’) trees. Pineapple sweet orange roots absorbed twice as much 14C from bromacil, and accumulated three times as much in the leaves, as did Cleopatra mandarin. The amount of conjugated metabolites formed was the same in the roots of the two cultivars, but twice as much formed in the leaves of Cleopatra mandarin as in the leaves of Pineapple sweet orange. The principle metabolite was 5-bromo-3-sec-butyl-6-hydroxymethyluracil; a minor metabolite was tentatively identified as 5-bromo-3-(3-hydroxyl-1-methylpropyl)-6-methyluracil. No 5-bromouracil was detected. Citrus cultivars differ in their ability to accumulate and metabolize bromacil into conjugated nonphytotoxic compounds.

Experiments were conducted in order to establish the mechanism by which the synergist MZH 2091 increases metribuzin activity on ivyleaf morningglory. Herbicide absorption and metabolism were compared for plants treated either with 14C-metribuzin alone or with 14C-metribuzin plus nonlabeled MZH 2091. The compounds were applied via the roots for 3 h and the absorption was determined. After the pulse treatment, the plants were grown for additional 0, 3, 6, 9, 12, 21, 45, or 69 h in water, and the metribuzin metabolism was studied in the cotyledons. The synergist did not interfere with herbicide uptake but did strongly inhibit metribuzin metabolism. The pathway of metribuzin metabolism in ivyleaf morningglory is discussed as well as the way it is affected by the synergist MZH 2091.

Partially purified glutathione-s-transferase (GST) isolated from corn (Zea mays L.) seedlings was about 14-fold higher in specific activity than GST isolated from giant foxtail (Setaria faberi Herrm. # SETFA) seedlings. Greater amounts of GST activity were present in leaf tissue than in stem tissue. Four-leaf giant foxtail seedlings contained about threefold more reduced glutathione per gram fresh weight in the leaves than one- to two-leaf giant foxtail seedlings. When atrazine and reduced glutathione were used as substrates, tridiphane [2-(3,5-dichlorophenyl)-2-(2,2,2-trichloroethyl)oxirane] inhibited isolated GST from corn with an I50 of about 5 μM and from giant foxtail with an I50 slightly lower. Tridiphane inhibited the metabolism of atrazine [6-chloro-N-ethyl-N′-(1-methylethyl)-1,3,5-triazine-2,4-diamine] to water-soluble metabolites in giant foxtail leaves but not in corn leaves. Unmetabolized atrazine levels tended to be greater in giant foxtail seedlings treated with tridiphane plus atrazine than in plants treated with atrazine alone. Tridiphane applied 12 h before atrazine increased the uptake of atrazine in both corn and five-leaf giant foxtail seedlings. The amount of atrazine metabolism to water-soluble metabolites increased in corn leaves but remained constant in giant foxtail leaves when atrazine uptake was increased. Tridiphane and atrazine combinations impaired net photosynthetic rates more than atrazine alone in giant foxtail seedlings but did not increase chlorophyll fluorescence. There was no decrease in net photosynthetic rate 12 h following applications of atrazine or tridiphane plus atrazine on corn leaves. Tridiphane did not decrease photosynthesis or increase chlorophyll fluorescence in either species when applied alone.

14C-labeled 4-amino-6-(1,1-dimethylethyl)-3-(ethylthio)-1,2,4-triazin-5(4H)-one (ethiozin)3 was metabolized more rapidly in tolerant than in sensitive wheat, Triticum aestivum L., cultivars. After a 6-h herbicidal pulse, the main metabolites were conjugates at all incubation times up to 48 h. The levels of deaminated and dethioethylated metabolites never exceeded 4% of the extractable radioactivity and also did not differ between tolerant and sensitive plants. On the contrary, 92% of the extractable radioactivity was in conjugates after 24 h in the leaves of tolerant plants compared to 25% in the leaves of sensitive plants. The differently sensitive wheat cultivars conjugated metribuzin, 4-amino-6-(1,1-dimethylethyl)-3-(methylthio)-1,2,4-triazin-5(4H)-one, at about half the rate that was observed with ethiozin. This finding may explain the fact that most wheat cultivars are more sensitive to metribuzin compared with ethiozin.

Radiolabeled (14C) 2-[4-(3-chloro-5-trifluoromethyl-2-pyridinyloxy)phenoxy] propionic acid (Compound C); its methyl-,n-butyl-, and ethoxyethyl-esters; and fluazifop-butyl {(±)-butyl 2-[4-[(5-(trifluoromethyl)-2-pyridinyl)oxy] phenoxy] propionate} were applied to the primary shoots of young rhizomatous quackgrass [Agropyron repens (L.) Beauv. # AGRRE]. Plants were sampled from 0.5 to 24 days after treatment (DAT) and analyzed for radiochemical. All treatments caused phytotoxic symptoms in primary shoots, rhizomes, and tillers and significantly reduced growth of primary shoots and rhizomes. Treatment with compound C or its methyl and butyl esters eliminated regrowth from all rhizomes excised from treated plants. The ethoxyethyl-ester and fluazifop-butyl controlled regrowth from rhizomes from 50% of the plants and substantially reduced shoot regrowth from the remainder. Rhizomes that did produce shoots contained significantly less radiochemical than those from which no regrowth occurred. At 24 DAT, a maximum of only 1% of each radiochemical applied was translocated to the first tiller and rhizomes and had been sufficient to cause marked phytotoxic symptoms. Soon after application (1 DAT), the major metabolites in the treated leaves and remainder of the plant for all compounds were the free acid and substantial amounts of polar conjugates that were hydrolyzable to the free acids. Radiochromatography of extracts from rhizomes and first tillers from all treatments gave similar chemical profiles, with the free acids and their conjugates as the predominant components present. These results provide evidence that esters of the pyridinyloxyphenoxypropionic acids are rapidly hydrolyzed after absorption by quackgrass; the free acids are then translocated and are the active form of these herbicides.

The uptake, distribution, and metabolism of diuron [3-(3,4-dichlorophenyl)-1,1-dimethylurea] by sugarcane (Saccharum officinarum L.) cultivars ‘PR980’ and ‘PR1048’ were determined 3 and 10 days after root treatment with 18.4 μM 14C-ring-labeled diuron. Uptake and distribution did not account for the differential tolerance of the two cultivars to diuron. Concentration of unmetabolized diuron was higher in the shoot and root of susceptible cultivar PR1048 than in tolerant cultivar PR980 at 3 and 10 days after treatment. The predominant metabolic pathway for diuron metabolism in both susceptible and tolerant sugarcane cultivars appeared to be the formation of mono-methyl diuron and its conjugation. The metabolic process was more rapid in PR980 than PR1048, apparently accounting for the tolerance of PR980.

Given k ≥ 2, we construct a (2k − 2)-parameter family of properly embedded minimal surfaces in ℍ2 × ℝ invariant by a vertical translation T, called saddle towers, which have total intrinsic curvature 4π(1 − k), genus zero and 2k vertical Scherk-type ends in the quotient by T. Each of those examples is obtained from the conjugate graph of a Jenkins–Serrin graph over a convex polygonal domain with 2k edges of the same (finite) length. As limits of saddle towers, we obtain properly embedded minimal surfaces, called minimal k-noids, which are symmetric with respect to a horizontal slice (in fact they are vertical bi-graphs) and have total intrinsic curvature 4π(1 − k), genus zero and k vertical planar ends.

We characterize conjugation classes of Christoffel words (equivalently of standard words) by the number of factors. We give several geometric proofs of classical results on these words and sturmian words.

The conjugative transfer of F-plasmids is repressed by a two-component system, which consists of the antisense RNA FinP and the protein FinO. FinO binds FinP, protecting it from endonucleolytic degradation and facilitating duplex formation between FinP and its complementary RNA. Here we present the results of site-specific protein–RNA crosslinking and gel-based fluorescence resonance energy transfer (gelFRET) experiments used to probe the structure of a complex of FinO bound to an RNA target consisting of a duplex with 5′ and 3′ single-stranded tails. The crosslinking experiments reveal that an extensive, largely positively charged surface on FinO contacts RNA. The gelFRET measurements indicate that the 5′ single-stranded tail of the RNA is in closer contact with much of the protein than the distal, blunt end of the RNA duplex. These data suggest that significant conformational adjustments in the protein and/or the RNA accompany complex formation.