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We introduce a new class of Banach spaces, called generalized-lush spaces (GL-spaces for short), which contains almost-CL-spaces, separable lush spaces (specially, separable C-rich subspaces of C(K)), and even the two-dimensional space with hexagonal norm. We obtain that the space C(K, E) of the vector-valued continuous functions is a GL-space whenever E is, and show that the GL-space is stable under c 0 -, l 1 -and l ∞ -sums. As an application, we prove that the Mazur-Ulam property holds for a larger class of Banach spaces, called local-GL-spaces, including all lush spaces and GL-spaces. Furthermore, we generalize the stability properties of GL-spaces to local-GL-spaces. From this, we can obtain many examples of Banach spaces having the Mazur-Ulam property.2010 Mathematics Subject Classification. Primary 46B04; Secondary 46B20,46A22. 1 2 DONGNI TAN, XUJIAN HUANG, AND RUI LIU Recently in [3], Cheng and Dong considered the extension question of isometries between unit spheres of Banach space and introduced the Mazur-Ulam property:Definition 1.2. A Banach space E is said to have the Mazur-Ulam property (briefly MUP) provided that for every Banach space F , every surjective isometry T between the two unit spheres of E and F is the restriction of a linear isometry between the two spaces.Cheng and Dong attacked the problem for the class of CL-spaces admitting a smooth point and polyhedral spaces. Unfortunately their interesting attempt failed by a mistake at the very end of the proof (also see the introduction in [10,28]). In [10], Kadets and Martín proved that finite-dimensional polyhedral Banach spaces have the MUP. Notice that the problem is still open even in two dimension case. In [28], the authors Tan and Liu proved that every almost-CL-spaces admitting a smooth point (specially, separable almost-CL-spaces) has the MUP.Recall that R. Fullerton [8] first introduced the notion of CL-spaces. It was extended by Lima [14,15] who introduced the almost-CL-spaces and gave the examples of real CL-spaces which are L 1 (µ) and its isometric preduals, in particular C(K), where C(K) is a compact Hausdorff space. The infinite-dimensional complex L 1 (µ) spaces are proved by Martín and Payá [20] to be only almost-CL-spaces. Lush spaces were introduced recently in [1] and have been extensively studied recently in [2,10,11]. Such spaces are of importance to supply an example of a Banach space E with the numerical index n(E) < n(E * ). It thus gives a negative answer to a question which has been latent since the beginning of the theory of numerical indices in the seventies. Now, a natural and interesting question is: "Does every almost-CL-space, even every lush space, has the MUP? "In this paper, we introduce a natural concept of generalized-lush spaces (GL-spaces for short), which contains almost-CL-spaces, separable lush spaces (specially, separable C-rich subspaces of C(K)), and even the two-dimensional space with hexagonal norm. We obtain that the space C(K, E) of the vector-valued continuous functions is a generalized-lush s...

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A field survey was conducted in 2014 to determine the response of Palmer amaranth (Amaranthus palmeri S. Wats.) populations from 16 counties in southcentral Kansas to commonly used herbicides. The main objective was to evaluate the sensitivity of 28 randomly collected populations to field-use rates of glyphosate, chlorsulfuron, 2,4-D, dicamba, atrazine, and mesotrione herbicides; and further characterize the sensitivity levels in two populations. The response of all tested populations was categorized as less sensitive (≤59% injury), moderately sensitive (60-89% injury), and susceptible (90-100% injury) based on visible injury at 21 days after treatment (DAT). Results from herbicide screening experiments indicated that 47, 36, 7, 75, and 32% of tested populations were less sensitive (putative resistant) to glyphosate, chlorsulfuron, 2,4-D, atrazine, and mesotrione herbicide, respectively. None of the tested populations showed less sensitivity (≤59% injury) to dicamba herbicide. Whole plant dose-response assays on two populations collected from Kiowa (KW2) and Pratt (PR8) counties indicated that the KW2 population had 3.0-, 2.3-, 5.8-, and 8.4-fold less sensitivity to 2,4-D, chlorsulfuron, atrazine, and mesotrione, respectively, compared to a known susceptible (MHS) population. In contrast, the PR8 population was 2.0-, 8.6-, 10.6-, 3.7-, and 2.8-fold less sensitive to 2,4-D, glyphosate, chlorsulfuron, atrazine, and mesotrione, respectively, compared to MHS population. Overall, these results suggest that reduced sensitivity to glyphosate, chlorsulfuron, atrazine, and/or mesotrione is highly prevalent in southcentral Kansas. Growers should adopt diversified weed control methods to manage these difficult-to-control populations on their production fields.Abbreviations: CI, confidence interval; DAT, days after treatment; GR 50 , 50% shoot biomass reduction; HR, herbicide-resistant; MOA, mechanism of action; SI, sensitivity index.