Abstract
Objective To investigate the effects of plyometric training on lower limb explosive power, agility qualities, and other sport-specific attributes of volleyball players, and to provide scientific methods for volleyball training. Methods Thirty volleyball players were randomly selected and divided into an experimental group and a control group (n=15 each) using the random number table method. The groups underwent 8 weeks of plyometric training (including 30–40 cm drop jumps, 50–60 cm box jumps, etc.) and traditional resistance training (including barbell squats, bench press, deadlifts, etc.), respectively. Before and after training, athletes' jumping ability was assessed via the standing long jump and vertical jump reach; movement ability was evaluated using the 30 m sprint and "T" drill; rapid change-of-direction ability was measured through the Nebraska test and Illinois test; movement transformation ability was tested using 15 s burpees, crawl and hurdle jump, and 15 s lateral shuffle; and coordination and control ability was examined through the quadrant jump, hexagon jump, and hex ball grab. The test results of lower limb explosive power (jumping ability, movement ability) and agility qualities (rapid change-of-direction ability, movement transformation ability, coordination and control ability) were compared between the two groups before and after the intervention. Results Before training, no significant differences were observed in any indicators between the two groups (P>0.05). After training, regarding lower limb explosive power, the experimental group showed significantly greater improvements in both jumping performance and movement performance indicators compared with the control group (P<0.05). In terms of agility qualities, the experimental group demonstrated superior performance in rapid change-of-direction ability tests, including the Nebraska test and Illinois test (P<0.05). For movement transformation ability, both groups exhibited similar effects in the 15 s burpees and crawl and hurdle jump tests (P>0.05), whereas the experimental group held a significant advantage in the 15 s lateral shuffle test (P<0.01). In coordination and control ability tests, plyometric training produced significantly better results than traditional resistance training in the quadrant jump, hexagon jump, and hex ball grab (P<0.05). Conclusion Plyometric training exerts significant effects on enhancing lower limb explosive power and agility qualities in volleyball players. Compared with traditional resistance training, plyometric training demonstrates notable advantages in volleyball-specific qualities such as vertical jumping, complex change-of-direction, and coordination control. This training modality holds important practical significance for strengthening athletes' lower limb muscle power and improving their rapid response capabilities.
Full Text
Preamble
Machine learning and deep learning methodologies have become essential tools in contemporary scientific computing. $ ( % & ’ ( ) ) * (-./0102345/67389::7.0;<0=-6/.=1 jE@"!> RE"! a5D">B>H >?@!?B"??QQM /1"A..8"?BBB#!9)9">B>H"B!"B>> pVqrstuvwxy[O\ 4]z{|}+l~(cid:127)S 6??!G(cid:150)H> $ The theoretical framework underlying these approaches relies on sophisticated mathematical formulations that describe complex computational graphs and optimization landscapes. $ vwx~r‚„(cid:127) )B ”IJo(cid:226)·!PQ~r(cid:144)ˆ(cid:140)YDcm(cid:142)(cid:143) ˆ=(cid:148)Qˆ!˚ˆ ?H ”!c(cid:148)(cid:154)(cid:155)m# ( (cid:213)T(cid:213)(cid:212)—(cid:214)j(cid:141)(cid:239)(cid:240)& RS )B L!B 03 T(cid:130)TU%HB L MB 03(cid:130)(cid:151)T:’ =fi˘V(cid:253)((cid:239)(cid:240)& RSWXUY%ZØ%[\:’ " (cid:239)(cid:240)æN!(cid:192)`]˝(cid:230)ˇT^% ]˝_T‘UB(cid:142)o(cid:226)·Ta0(!’ )B 3 Y(cid:212)–%( b) c(cid:201)d–e/f(cid:226)0($ Recent advances in neural network architectures have demonstrated remarkable capabilities across diverse application domains. $(cid:239)(cid:240)N!@i(cid:181)R~((cid:139)¨!¶(cid:143)ˆ TTa]0=f(cid:226)]0›(cid:212)Trt(cid:218)¤S(cid:142)(cid:143)Uz(cid:148)Qˆ& 9sB"BH’ " @KLMN(cid:139)¨!h(cid:212)(cid:201) d0(B(cid:142)D!¶(cid:143)ˆ@ R6U:2.P2B(cid:142)%V@@A8EA.B(cid:142):(cid:190)¢“u& 9sB"BH’ $
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Theoretical Foundations
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Key theoretical results include: (1) a proof of convergence for the proposed algorithm under standard assumptions; $WA8D!Oac’+E8DU68"’E::6@2,AE8 U6,F668 :2-A7 .,:6,0+A8D0E3-E587 ,:2A8A8D287 @EF6:@A3U .-60AGA0K52@A,A6.EGJE@@6\U2@@-@2\6:.( d) " ’+A86.61E5:82@EG2--@A67 360+28A0.!>B>H!!>$ (2) derivation of generalization bounds for the learned models; and (3) analysis of computational complexity. $ A80@57A8D)B =!B 03UE4153-A8D76-,+ 287 HB =MB 03UE4153-A8D% 287 ,:27A,AE82@:6# .A.,2806,:2A8A8D$ These contributions establish a rigorous theoretical basis for practical deployment. $ 153-A8D2UA@A,\287 3EJ6368,2UA@A,\% 287 2DA@A,\ $
CAD System Integration
Modern CAD systems increasingly incorporate machine learning components to enhance design automation. $ 9oB"BH% "aG,6:,:2A8A8D!,+664-6:A368,2@D:E5- .+EF67 .AD8AGA# 028,@+AD+6:A3-:EJ6368,.A8 153-A8D287 3EUA@A,\A87A02,E:.A8 ,6:3.EG@EF6:@A3U 64-@E.AJ6-EF6:0E3# -2:67 ,E,+60E8,:E@D:E5- $ The ability to predict design parameters from functional specifications significantly reduces development cycles. $ 9oB"BH% !287 ,+664-6:A368,2@D:E5- +27 2.AD8AGA# 028,27J28,2D6A8 ,+6?H#.60E87 :6-62,67 +E:AlE8,2@.,6- ,6.,$ Our methodology employs deep neural networks to learn complex mappings between design spaces. $ 9s B"BH% "(3/=741.3/h2-A7 .,:6,0+A8D0E3-E587 ,:2A8A8D+2.2.AD8AGA028,6GG60,A8 A3-:EJA8D,+664-@E.AJ6 -EF6:287 2DA@A,\EGJE@@6\U2@@-@2\6:.n@EF6:@A3U."’E3-2:67 FA,+ ,:27A,AE82@:6.A.,2806,:2A8A8D! :2-A7 .,:6,0+A8D0E3-E587 ,:2A8A8D+2..AD8AGA028,27J28,2D6.A8 JE@@6\U2@@.-60AGA0K52@A,A6..50+ 2.J6:,A02@ 153-A8D!0E3-@647A:60,AE82@0+28D6.!287 0EE:7A82,67 0E8,:E@"O+A.,:2A8A8D36,+E7 +2.A3-E:,28,-:20,A# 02@.AD8AGA02806GE:68+280A8D2,+@6,6.n@EF6:@A3U 35.0@6.,:68D,+ 287 A3-:EJA8D,+6A::2-A7 :6.-E8.62UA@# I0C D35;1":2-A7 .,:6,0+A8D0E3-E587 ,:2A8A8D’ ,:27A,AE82@:6.A.,2806,:2A8A8D’ JE@@6\U2@@-@2\6:’ @EF6: @A3U 64-@E.AJ686..’ 2DA@A,\ *F‹:Yl(cid:152)J¨H&(cid:139)0´Q-e!0:Yx (cid:238)”P(cid:247).(cid:215)—–I(cid:247)(cid:147)# (cid:150)˜NQ(cid:219)(cid:218)o!:Y x(cid:150)(cid:223)`xQ(cid:147)(cid:219)&J(cid:230)Ya(cid:150)n.D&Y(cid:218)!x d(cid:218)(cid:242)(cid:219)(cid:218)Q(cid:146)Qmª(?) # (cid:150)F‹:YxQ”⁄¨ #(cid:253)(cid:217)!—(cid:149)´(cid:142)G¨#5"˘I(cid:255)(cid:247)K(cid:192)(>) # (cid:255) K¨#NO(cid:246)(cid:247)(cid:143)(cid:144)(cid:220)(cid:221)£(cid:222)&(cid:223)(cid:212)&(cid:224)/!l_(cid:138) (cid:224)Æ(cid:146)5QNOv_(cid:139)(cid:224)ÆG‘+’G()#!) # ˙(cid:160)!
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The implementation utilizes specialized convolutional architectures for processing geometric data. $N__V&(??) (cid:143)(cid:144)p "(cid:242)…&«(cid:242)(cid:147)O+£(cid:222)(cid:147)(cid:219)&º(cid:181)!!(cid:255)J(cid:230)IS S3¨#WlXØ(cid:192)ak‹:YxQ(cid:138)(cid:230)+(cid:147)(cid:219)⁄ G# ˙(cid:160)!k‹:YoQ…Y&(cid:147)(cid:219)&Y(cid:218)aF‹:
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Empirical Evaluation
Comprehensive experiments were conducted using standard CAD benchmarks. $ 9oB"BH% # , ?(cid:210)mD=(cid:211)B(cid:212)% y6& O2U"?T2.A0A8GE:32,AE8 EG,+6.5U160,.$ The evaluation metrics include R-squared (R²) scores, computational time, and robustness measures. $ PD3=> % ?QM"QH y)"!> M9"?H y)"?) ?QM")( y>">Q M("!> y>"!H >>"QQ y?"!> >>"!? y>"B> %"!"(cid:213)m«(cid:214) º(cid:181)œ"–FÆ(cid:151)øQ eajNOchRa]cf_ PF‹œ!‡2¨(cid:181)n(cid:150)(cid:138)(cid:204)(cid:240)(cid:137)º(cid:181)(cid:204)(cid:212)fF(cid:239) KQº(cid:181)Fœ# p ?º(cid:181)Fœ CAD"?I+E6.5.67 GE:,6.,A8D _P(cid:252)‰$ The dataset encompasses diverse design examples from multiple engineering disciplines. $SOhag% "(cid:150)7 ´ B"B? .!„ŁJ(cid:230)(cid:240)Y&(cid:176)…+S(cid:192)7⁄!F(cid:159)n (cid:236)~:º(cid:181)o:Yx`x(cid:213)(cid:242)Y(cid:218)Q(cid:204)(cid:223)$
Results indicate that the proposed framework achieves state-of-the-art performance across all evaluation criteria. $ (cid:252)D eg)9>HB!œß jV’c% "57 HB 3!(cid:192)n(cid:137)(cid:150)7d y? 33$ Comparative analysis with conventional methods reveals significant advantages. $ (cid:148).D…(cid:142)e(cid:192)(cid:223)<% !(cid:236) Cº(cid:181)(cid:149)(cid:145)>?(cid:237)(cid:243)$ Ablation studies confirm the contribution of each architectural component. $ p >U% # (cid:254)Iº‘(cid:215)$
Advanced Architectures
Further developments extend the basic framework to handle more complex scenarios. $dVN% " I7º¨(cid:214)(cid:204) ?"> L)"( 3!oŁI(cid:150)7(cid:226)G—(cid:214) <=>?"+,,-." //0123"41,5"675"08@ABCD"EFGHHI ! ! " ¡Œ!&"J(cid:230)ISS3¨#aF‹:YxP(cid:190)_(cid:243)P(cid:247)Qm“=; 9H) (cid:215)!º‘(cid:150)7 yB"H 03! ·aB”…Y~:ˆTI 7!(cid:157)IW(cid:143)(cid:144))(cid:255)K(cid:204)(cid:134)4(cid:152)fŁ!F(cid:159)º(cid:181)8fl (cid:254)Ix!$ Multi-scale feature extraction enables processing of designs at different resolutions. $!{w%(cid:147)E§(cid:157)J=(cid:159) ?(B §# 0(cid:216)2"(cid:128)(cid:129)d" ( (cid:246)Q—(cid:149)´(cid:142)G¨#!{(cid:246) ¨#§(cid:157)+(cid:204)5a(cid:181)Æ2æ^# ¨#HI1 G‘¨ #UV2 ˝’p"!¨#(cid:239)(cid:160)—Ł(cid:220)(cid:221)£(cid:222)&(cid:223)(cid:212)&(cid:150) fl!(cid:131)&o’G¨## (cid:220)(cid:221)£(cid:222){ § ) 2! { 2 ( §![r(cid:255)‘d…(cid:238)”(cid:255) HB[!{ > (cid:246)(cid:138) H[!£ (cid:222)(cid:204)E(cid:204)a(cid:140)K(cid:156)!(cid:204)…@DV’p!P(cid:222)(cid:204)(cid:217)m¨ Jz(cid:204)…!5-(fl!(cid:134)(cid:230)P(cid:222)(cid:134)6BaK((cid:150)(cid:129)(cid:137) (cid:153)(cid:230)[(cid:238)!vt(cid:181)˝(cid:150) > L) .’(cid:223)(cid:212){§ ) 2!{2 ( §!(cid:255)‘L…(cid:238)”(cid:255) )B[pr!{ > (cid:246)(cid:138) )[!(cid:150) )(cid:150)(cid:223)(cid:212)]!E(cid:224)+(cid:220)(cid:221)!+ L) 03(cid:151)(cid:137)FG(cid:212)[(cid:134)(cid:224)# Ifl!vt > L) .’(cid:150)fl{§ ) 2!{2 M §!(cid:255)‘L …(cid:238)”(cid:255) MB[pr!{ > (cid:246)_(cid:138) H[!E(cid:204)a(cid:140)K(cid:156) ?«!-(cid:238)+(cid:220)(cid:221)!5-(fl!gFB-aJ-G‘ u(cid:220)(cid:221)(cid:224)†fl[(cid:134)(cid:238)”fl«(cid:137)(cid:224)†(cid:213)P!vt ) L ! .#(cid:135)V!{(cid:246)~F > § )B 3A8 Q H P3(cid:134)(cid:230)†…(cid:218) d’G¨#! …(cid:204)(cid:230)7ßa(cid:150) » 6 (cid:176) c Q MB[ L QB[!.(cid:130)(cid:176)c<ºfŁ˜(cid:204)<(cid:181)# dCD‡2¨ #Y(cid:146)5&(cid:136)!:;»(cid:216)Æ(cid:148)(cid:148)æ”⁄NW$ Hierarchical attention mechanisms capture dependencies across design elements. $c+a0(cid:204)(cid:223) (cid:128)(cid:129)‘(cid:224)w(cid:130)a/o# ¨#(cid:146) 5 $
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Conclusion
This work presents a comprehensive mathematical and computational framework for integrating deep learning with CAD systems. $(cid:148)!(cid:147)£#n(cid:150)¨#(cid:140)"!)B L!B 03 Q(cid:147)" I7&{2 ?B §&˜K(cid:224)5(cid:247)(cid:147)&øPø3EFd (cid:239)0(cid:231)=(cid:139)7!f(cid:242)d(cid:139)7n(cid:157) B"M’(cid:128)(cid:154)(cid:139)(cid:224)"!
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The established theoretical foundations provide guidance for developing next-generation learned design systems. $ &L&% +Y(cid:218)(cid:247)(cid:147)!J(cid:230)xz§.D…!~:xvtQ(cid:204)(cid:223)# p HR6U:2.P2º(cid:181)JK(cid:127)(cid:190)p CAD"HI0+632,A07A2D:23EGR6U:2.P2,6.,.A,6 V@@A8EA.º(cid:181)(>?) "(cid:246)(cid:247)(cid:132)‘ST(cid:149)(cid:145).Deq+ (cid:238)”Q(cid:243)ˆ(cid:237)# (cid:150)(cid:148)p M ~(cid:127)Qº(cid:181)JK(cid:239)!:Y xH§}4F$ We anticipate broad impact across manufacturing, engineering, and related fields. $ p ?B% "(cid:246)(cid:247)EF(cid:238)”Q(cid:150)z(cid:181) ˝+(cid:219)(cid:223)(cid:214)(cid:156)⁄G# (cid:150)(cid:141)‹/JK(cid:239)!:YxCt (cid:141)‹/Q‹(cid:128)(cid:129)(cid:147)(cid:219)!~:`xM ) +$
References
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